EXPERIMENTAL AND NUMERICAL STUDIES OF AEROSOL

PENETRATION THROUGH SCREENS

A Dissertation

by

TAE WON HAN

Submitted to the Office of Graduate Studies of Texas A&M University

in partial fulfillment of the requirements for the degree of

DOCTOR OF PHILOSOPHY

May 2007

Major Subject: Mechanical Engineering

EXPERIMENTAL AND NUMERICAL STUDIES OF AEROSOL

PENETRATION THROUGH SCREENS

A Thesis

by

TAE WON HAN

Submitted to the Office of Graduate Studies of Texas A&M University

in partial fulfillment of the requirements for the degree of

DOCTOR OF PHILOSOPHY

Approved by: Chair of Committee, Andrew R. McFarland Committee Members, John S. Haglund

Sridhar Hari Yassin A. Hassan

Head of Department, Dennis L. O’Neal

May 2007

Major Subject: Mechanical Engineering

iii

ABSTRACT

Experimental and Numerical Studies of

Aerosol Penetration through Screens. (May 2007)

Tae Won Han, B.S., M.S., Keimyung University, Korea;

M.S., Texas A&M University

Chair of Advisory Committee: Dr. Andrew R. McFarland

This research reports the results of experimental and numerical studies performed

to characterize aerosol deposition on four different types of commercially available

screens (electroformed-wire, woven-wire, welded-wire, and perforated-sheet) over a wide

range of Stokes numbers (Stk ~ 0.08 to 20) and Reynolds numbers (ReC ~ 0.5 to 575). The

objective of the present research was to use the results of the study to develop models and

data that will allow users to predict aerosol deposition on screens. Three-dimensional

Computational Fluid Dynamics (CFD) simulations using Fluent (version 6.1.22), as a tool,

were undertaken and thus validating the numerical technique and then the result has been

compared with the experimental data. For each type of screen, results showed that

beginning at critical value of Stokes number where efficiency increased gradually to its

maximum value that was almost asymptotic to the areal solidity. It is shown that data

obtained from experimental and numerical studies for one particular type of screen would

collapse to a single curve if the collection efficiency is expressed in terms of non-

dimensional parameters.

iv

Correlations characterizing the aerosol deposition process on different types of

screens were developed based on the above methodology. The utility of the developed

procedure was demonstrated by considering an arbitrary test case, for a particular

condition and reconstructing the efficiency curve for the test case. Further, results of the

current study were compared with earlier researchers’ models (Landahl and Hermann,

1949; Davies, 1952; Suneja and Lee, 1974; Schweers et al., 1994) developed for aerosol

deposition on fibrous filters and discussed. These results suggest that the aerosol

collection characteristic on different models is different and depends on the nature of the

manufacturing process for a typical model (wire or fiber).

Finally, the pressure coefficient (Cp) for flow across the screen can be expressed

as a function of the Reynolds number (ReC,f) and the fraction of open area (fOA).

Correlations expressing the actual relationships were evolved. Additionally, a model was

developed to relate pressure coefficient in terms of correction factor ( ) and Reynolds

number.

OAfG

v

DEDICATION

To my family

vi

ACKNOWLEDGMENTS

My research is very much the product of a sustained collective endeavor and love.

During my research over the part several years I have received enormous support and

encouragement from the faculty, staff and fellow graduate students of Texas A&M

University, the Mechanical Engineering Department’s Aerosol Technology Laboratory.

First of all, I would like to express my deepest gratitude to Dr. Andrew R. McFarland for

his guidance, enthusiasm, and support throughout the course of this research. He is a

great scientist, engineer, instructor and leader in aerosol science. I wish to thank him for

all the opportunities he has made available to me in the pursuit of my Ph.D. degree and

for always motivating me to perform my best.

I have also been blessed to benefit from the many fruitful discussions and

suggestions from Dr. Sridhar Hari regarding this research. I would also like to extend my

thanks to Dr. John S. Haglund. His engineering insight and intuition are truly remarkable.

I am also grateful to Dr. Yassin A. Hassan who served as a member of my committee and

provided comments and suggestions for improving this manuscript.

Special thanks and respect is extended to Mr. Carlos A. Ortiz in the Energy

Systems Laboratory for his helpful, stimulating, and encouraging comments. I wish to

thank Charlotte D. Sims for her editing skills. I would also like to thank my past advisors,

Dr. Dennis O'Neal from Texas A&M University and Dr. Sung-Hoon Kim from

Keimyung University in Korea, who provided me with tremendous encouragement for

my life.

Many thanks to YoungJin Seo and other laboratory colleagues in the Mechanical

Engineering Department for their help and encouragement. Additionally, I would like to

vii

thank Mr. Nene for the detailed flow disturbance velocity and turbulent intensity

measurements at various sampling locations presented in my study.

This thesis could not have been done without the sacrifices and support of my wife;

Soo-Kyoung Bae. I am dedicating my small accomplishment to her, my daughter, my

parents, and parents-in-law.

Finally, I thank Almighty God for all His blessings and presence in my life.

viii

TABLE OF CONTENTS

Page

ABSTRACT…………......................................................................................... iii

DEDICATION..................................................................................................... v

ACKNOWLEDGMENTS................ ................................................................... vi

TABLE OF CONTENTS..................................................................................... viii

LIST OF FIGURES................. ............................................................................ x

LIST OF TABLES............................................................................................... xvii

LIST OF SYMBOLS........................................................................................... xix

CHAPTER

I INTRODUCTION ............................................................................... 1

Background ................................................................................... 1 Objectives of the Present Study ..................................................... 4 Layout and Key Points in Each Chapter ........................................ 6

II THEORETICAL BACKGROUND ..................................................... 9

Description of the Filter Models for the Flow Field ...................... 9 Single Fiber Efficiency Concept..................................................... 12 Capture Mechanisms ...................................................................... 13 Summary of Earlier Researchers’ Results ..................................... 16 Pressure Drop Across Screens ....................................................... 21

III DESCRIPTION OF SCREENS............................................................ 23

Wire Screen..................................................................................... 23 Perforated-Sheet Screen.................................................................. 28

IV EXPERIMENTAL STUDIES ............................................................. 31

Aerosol Generator ......................................................................... 32

ix

CHAPTER Page Aerosol Size Distribution and Measurement of Aerosol Particle Size ............................................................................................ 32 Experimental Methodology ........................................................... 33 Experimental Results ..................................................................... 48 Discussion of Errors........................................................................ 55 V NUMERICAL STUDIES .................................................................... 60

Flow Field Simulation ................................................................... 62 Particle Tracking Methodology ..................................................... 64 Numerical Results.......................................................................... 65 VI COMPARISON OF EXPERIMENTAL AND NUMERICAL STUDIES…………………………………………………………….. 84

Comparison with Actual Efficiencies ........................................... 85 Actual Efficiency Modeling .......................................................... 90 Modeling for Standardized Screen Efficiency............................... 104 Comparison with Previous Studies ............................................... 117 Pressure Coefficient Modeling ..................................................... 119 VII APPLICATION TO THE PROBLEM OF AEROSOL COLLECTION ON A SCREEN ………………………………………………………. 129

VIII CONCLUSION AND FUTURE WORK ............................................. 136

Recommendations for Future Works ............................................ 137

REFERENCES ......... ......................................................................................... 139

APPENDIX-1 DEFINITION OF CHARACTERISTIC LENGTH FOR PERFORATED-SHEET SCREEN……...……………...…… 143

APPENDIX-2 TABLE OF CALCULATION OF COLLECTION EFFICIENCY ON A SCREEN……… .................................. 148

APPENDIX-3 SOFTWARE FOR THE DEPOSITION ON SCREENS ....... 150

VITA .............................. ................................................................................... 151

x

LIST OF FIGURES

FIGURE Page

1.1 Representative inlet samplers with screen .................................................. 1

2.1 Illustration of particle collection by a single fiber or wire through the interception and impaction mechanisms..................................................... 15 3.1 Electroformed-wire screen tested. Parameters in each figure are mesh

size (M), wire diameter (dw), and fraction of open area (fOA) ..................... 25

3.2 Woven-wire screen tested. Parameters in each figure are mesh size (M), wire diameter (dw), and fraction of open area (fOA) .................................... 26

3.3 Welded-wire screen tested. Parameters in each figure are mesh size (M), wire diameter (dw), and fraction of open area (fOA) .................................... 27 3.4 Schematic for the calculation of fraction of open area (fOA) on wire screen 27

3.5 Perforated-sheet screen tested. Parameters in each figure are hole diameter (dh) and fraction of open area (fOA) ............................................................. 29

3.6 Schematic for the calculation of fraction of open area (fOA) on perforated-sheet screen .............................................................................. 30

4.1 Photo of setup for screen test…………………………………………….. 34

4.2 Schematic of setup for screen test………………………………………... 35

4.3 Calibration result of Hi-Vol Blower using root meter (full flow ranges;

200-3000 L/min) and H-Q digital meter (low flow ranges; 200–1500 L/min) with U-tube and digital manometer…………………………….. .. 36

4.4 Normalized velocity profile and turbulent intensity at 0.7-duct diameter upstream of screen location. uAVG = 1.62 m/s, Std. Dev.AVG = 0.261, COV = 16.1%.…………………………………………………………….. 39 4.5 Normalized velocity profile and turbulent intensity at 1.0-duct diameter downstream of screen location. uAVG = 1.62 m/s, Std. Dev.AVG = 0.141, COV = 8.7%.…………………………………………………………….. . 40

xi

FIGURE Page

4.6 Normalized velocity profile and turbulent intensity at 0.7-duct diameter upstream of screen location with screen (16×16 Mesh, 0.018-inch, 0.51). uAVG = 1.59 m/s, Std. Dev.AVG = 0.225, COV = 14.2%……..…………..... 41 4.7 Normalized velocity profile and turbulent intensity at 1.0-duct diameter downstream of screen location with screen (16×16 Mesh, 0.018-inch, 0.51). uAVG = 1.64 m/s, Std. Dev.AVG = 0.082, COV = 5.0%……..……..... 42 4.8 Normalized velocity profile and turbulent intensity at 0.7-duct diameter upstream of screen location with screen (20×20 Mesh, 0.017-inch, 0.44). uAVG = 1.62 m/s, Std. Dev.AVG = 0.288, COV = 17.8%………....……....... 43 4.9 Normalized velocity profile and turbulent intensity at 1.0-duct diameter downstream of screen location with screen (20×20 Mesh, 0.017-inch, 0.44). uAVG = 1.60 m/s, Std. Dev.AVG = 0.055, COV = 3.4%…………...….…..... 44 4.10 Wall losses between screen holder and filter holder................................... 47 4.11 Actual efficiency as a function of Stokes number for electroformed- wire screen (45×45, 0.00138-inch, 0.88 ...................................................... 49 4.12 Actual efficiency as a function of Stokes number for electroformed- wire screen (20×20, 0.00257-inch, 0.90). .................................................... 49 4.13 Actual efficiency as a function of Stokes number for woven-wire screen (20×20, 0.017-inch, 0.436) .......................................................................... 50 4.14 Actual efficiency as a function of Stokes number for woven-wire screen (64×64, 0.0045-inch, 0.507). ....................................................................... 50 4.15 Actual efficiency as a function of Stokes number for woven-wire screen (16×16, 0.018-inch, 0.507). ......................................................................... 51 4.16 Actual efficiency as a function of Stokes number for woven-wire screen (30×30, 0.0095-inch, 0.511). ....................................................................... 51 4.17 Actual efficiency as a function of Stokes number for woven-wire screen (16×16, 0.016-inch, 0.554). ......................................................................... 52 4.18 Actual efficiency as a function of Stokes number for woven-wire screen (14×14, 0.017-inch, 0.581). ......................................................................... 52 4.19 Actual efficiency as a function of Stokes number for woven-wire screen (16×16, 0.0095-inch, 0.719). ....................................................................... 53

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FIGURE Page

4.20 Actual efficiency as a function of Stokes number for welded-wire screen (8×8, 0.017-inch, 0.746). ............................................................................. 53 4.21 Actual efficiency as a function of Stokes number for perforated-sheet screen (0.015-inch, 0.21). ............................................................................ 54 4.22 Actual efficiency as a function of Stokes number for perforated-sheet screen (0.1875-inch, 0.51). .......................................................................... 54 5.1 Schematic for the idealization of numerical analysis on the screen ........... 61

5.2 Schematic of the numerical setup used to study the screen deposition process......................................................................................................... 63

5.3 Result of the numerical model iteration...................................................... 67

5.4 Comparison of efficiency as a function of Stokes number between the ideal model (with symmetric boundary conditions) and the real model (with symmetric boundary condition) of numerical simulation with one of woven-wire screen (14×14 mesh, dw = 0.017-inch, fOA = 0.581)................ 69 5.5 Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for electroformed-wire screen (40×40, 0.00629-inch, 0.56). 70 5.6 Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for electroformed-wire screen (50×50, 0.00268-inch, 0.75). 71 5.7 Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for electroformed-wire screen (45×45, 0.00138-inch, 0.88). 72 5.8 Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for electroformed-wire screen (20×20, 0.00257-inch, 0.90). 73 5.9 Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for woven-wire screen (20×20, 0.017-inch, 0.436).…...…… 74 5.10 Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for woven-wire screen (64×64, 0.0045-inch, 0.507)..….….… 75 5.11 Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for woven-wire screen (16×16, 0.018-inch, 0.507)….….…. 76 5.12 Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for woven-wire screen (30×30, 0.0095-inch, 0.511)............ 77

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FIGURE Page

5.13 Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for woven-wire screen (16×16, 0.016-inch, 0.554).............. 78 5.14 Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for woven-wire screen (14×14, 0.017-inch, 0.581).............. 79 5.15 Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for woven-wire screen (16×16, 0.0095-inch, 0.719)............ 80 5.16 Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for welded-wire screen (8×8, 0.017-inch, 0.746)................. 81 5.17 Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for perforated-sheet screen (0.017-inch, 0.21) ..................... 82 5.18 Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for perforated-sheet screen (0.072-inch, 0.51) ..................... 83 6.1 Comparison of actual efficiency predictions for electroformed-wires to experimental and numerical data (ReC = 0.5 to 30). Parameters in legend are mesh size, wire diameter (µm), and fraction of open area (fOA) ........... 86 6.2 Comparison of actual efficiency predictions for woven-wires to experimental and numerical data (ReC = 1 to 158). Parameters in label are mesh size, wire diameter (µm), and fraction of open area.................... 87

6.3 Comparison of actual efficiency predictions for woven-wires to experimental and numerical data (ReC = 1 to 158). Parameters in label are mesh size, wire diameter (µm), and fraction of open area.................... 88

6.4 Comparison of actual efficiency predictions for welded-wires to experimental and numerical data (ReC = 10 to 100). Parameters in label are mesh size, wire diameter (µm), and fraction of open area.................... 91 6.5 Comparison of actual efficiency predictions for perforated-sheet to experimental and numerical data (ReC = 10 to 575). Parameters in label are effective slack length (µm) and fraction of open area .......................... 90 6.6 The functions C1, C2, and C3 of Equation (6-1) for electroformed-wire screens......................................................................................................... 93 6.7 The functions C1, C2, and C3 of Equation (6-1) for woven-wire and

welded-wire screens.................................................................................... 93

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FIGURE Page

6.8 The functions C1, C2, and C3 of Equation (6-1) for perforated-sheet screens......................................................................................................... 94 6.9 Comparison between the experimentally and numerically measured actual efficiency and correlated actual efficiency based on correlation (Equation 6-3) for electroformed-wire screens........................................... 96 6.10 Comparison between the experimentally and numerically measured actual efficiency and correlated actual efficiency based on correlation (Equation 6-4) for woven-wire screens ...................................................... 97 6.11 Comparison between the experimentally and numerically measured actual efficiency and correlated actual efficiency based on correlation (Equation 6-5) for welded-wire screen ....................................................... 98 6.12 Comparison between the experimentally and numerically measured actual efficiency and correlated actual efficiency based on correlation (Equation 6-6) for perforated-sheet screens................................................ 98 6.13 Comparison of actual efficiency predictions for electroformed-wires to

experimental data (ReC = 0.5 to 30). Parameters in legend are mesh size, wire diameter (µm), and fraction of open area (fOA) .................................. 100

6.14 Comparison of actual efficiency predictions for woven-wires

(ReC = 1 to 158). Parameters in legend are mesh size, wire diameter (µm), and fraction of open area (fOA) .................................................................... 101

6.15 Comparison of actual efficiency predictions for welded-wires

(ReC = 10 to100)…………………….......................................................... 102

6.16 Comparison of actual efficiency predictions for perforated-sheet (ReC = 10 to 575). Parameters in legend are effective slack length (µm) and fraction of open area (fOA)…………………...……………………….. 103

6.17 Comparison of standardized screen efficiency predictions for four screens (a. electroformed-wire, b. woven-wire, c. welded-wire, and d. perforated-sheet) to experimental and numerical data................................ 105

6.18 Plot for verifying the standardizing data points with linear regression method ........................................................................................................ 106

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FIGURE Page

6.19 Comparison of actual efficiency predictions for woven-wires to experimental and numerical data with the same fraction of open area (0.51). Parameters in label are mesh size, wire diameter (µm) and fraction of open area................................................................................... 108

6.20 Comparison of standardized screen efficiency predictions for screens (a. electroformed-wire, b. woven-wire, and c. perforated-sheet) to experimental and numerical data................................................................. 111 6.21 Plot for verifying the standardizing data points with linear regression

method. Comparison between the standardized screen efficiency (ηSS) and correlated standardized screen efficiency (ηSS,i), (a)

electroformed-wire, (b) woven-wire, and (c) perforated-sheet..................... 112 6.22 Plot for analyzing the characteristic of screen performance as a function of Stokes number. Curves are provided by Equation (6-14)....................... 114 6.23 Comparison of standardized screen efficiency as a function of Stokes

number. Curves are provided by Equation (6-14) ........................................ 116

6.24 Comparison of standard screen efficiency for wire screens with those of the previous investigators’ models (ReC = 0.5 to 575).................................. 118

6.25 Pressure coefficient (Cp) as a function of wire Reynolds number (ReC,f)

for electroformed-wire screen, between 0.56 and 0.90 fraction of open areas ............................................................................................................ 120

6.26 Pressure coefficient (Cp) of experimental vs. numerical (a) and experimental vs. correlation (b) as a function of wire Reynolds number

(ReC,f) for woven-wire screen, between 0.436 and 0.719 fraction of open area ..................................................................................................... 121

6.27 Pressure coefficient (Cp) of experimental vs. numerical (a) and experimental vs. correlation (b) as a function of effective slack length Reynolds number (ReC,f) for perforated-sheet screen, between 0.21 and 0.51 fraction of open area..................................................................... 122

6.28 Cp/ as a function of wire Reynolds number (Re

OA

electroformed-wire screen, between 0.56 and 0.90 fraction of open area .. 124 fG C,f) for

6.29 Cp/ as a function of wire Reynolds number (Re

OA

screen between 0.436 and 0.719 fraction of open area............................... 125 fG C,f) for woven-wire

xvi

FIGURE Page

6.30 Cp/ as a function of effective slack length Reynolds number (Re

OA

for perforated-sheet screen, between 0.21 and 0.51 fraction of open area . 126 fG C,f)

6.31 Comparison of Cp/ as a function of Reynolds number (Re

OA

screens......................................................................................................... 128 fG C,f) for all

7.1 Comparison of the collection efficiency curves as a function of Stokes

number reconstructed based on the developed procedure to experimental data. Screen (M: 45×45, dw: 35 µm, αA: 0.12)…..………………….……. 132

7.2 Comparison of collection efficiency curves presented in Fig. 6-13 to the

new curves reconstructed based on the developed procedure for screens with intermediate solidity values. Screens (M: 34×34, dw: 132 µm, fOA: 0.68 and M: 36×36, dw: 71 µm, fOA: 0.81).…………..………………….… 135

xvii

LIST OF TABLES

TABLE Page

1.1 General information of wire and perforated-sheet screens ......................... 3

2.1 Single fiber efficiency due to interception mechanism ............................... 17

2.2 Single fiber efficiency due to inertial impaction mechanism ..................... 18

2.3 Single fiber efficiency due to interception plus inertial impaction mechanisms................................................................................................. 19

3.1 Specification of screens tested for this study.............................................. 24

3.2 Tolerances for woven-wire and perforated-sheet openings are specified by ASTM Standard E-11-04 ....................................................................... 28

3.3 Tolerances for hole diameter of perforated-sheet are specified by ASTM Standard E-323-80 .......................................................................... 30

4.1 The summary of average velocity and COV at each configuration ........... 38

4.2 Operation condition of experiment for each screen.................................... 47

4.3 Minimum and maximum wall losses for each screen................................. 46

4.4 The total predicted uncertainty in the calculated value of Stokes number for electroformed-wire ................................................................................ 58

4.5 The total predicted uncertainty in the calculated value of Stokes number for woven-wire............................................................................................ 59

4.6 The total predicted uncertainty in the calculated value of Stokes number for perforated-sheet ..................................................................................... 59

5.1 Operation condition of numerical simulations for each screen .................. 66

6.1 Values of C1, C2, and C3 in Equation (6-1) obtained by regression analysis 92 6.2 Values of z0, z1, z2, z3, z4, z5, and z6 in Equation (6-2) obtained by

regression analysis ...................................................................................... 94

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TABLE Page

6.3 Values of x0, x1, x2, and x3 in Equation (6-9) obtained by regression analysis....................................................................................................... 107

6.4 Values of Stk50, and x4 in Equation (6-10)................................................... 107

6.5 Values of β1, β2, and β3 in Equation (6-13) obtained by trial-and-error and the evaluation of linear regression........................................................ 110

6.6 The value of screen parameter for analyzing the characteristic of screen performance in Figure 6.24.......................................................................... 115

6.7 Summary of the values of G(fOA) and constants (A and B) for

Wakeland and Keolian (2003). and our data (ATL: Aerosol Technology Laboratory in TAMU) .................................................................................. 127

7.1 Result of actual efficiency that was reconstructed based on the application to the case problem-A on a screen (M: 45×45, dw: 35 µm, αA: 0.12) and compared with experimental results). ........................................................... 131 7.2 Additional calculations that present the collection efficiency value for

different sized particles estimated from the application to the problem on a screen (M: 34×34, dw: 132 µm, fOA: 0.68)………………………………… 135

xix

LIST OF SYMBOLS

a = Constant A = Constant AF = After-Filter AD = Aerodynamic Diameter ATL = Aerosol Technology Laboratory b = Constant B = Constant

c = Constant C = Relative aerosol concentration Ca = Cunningham’s slip correction factor based on the aerodynamic diameter CAF = After filter concentration Cc = Cunningham’s slip correction CD = Particle drag coefficient cf = Concentration of fluorescein in filter or screen sample (fluorometer reading) Ci = Reference concentration Co = Concentration after wall loss Cp = Cunningham’s slip correction factor based on the physical particle diameter Cp = Pressure coefficient CSM = Screen relative concentration C1, C2, C3 = Constants CFD = Computational Fluid Dynamics CS = Center-to-Center Spacing COV = Coefficient of Variation da = Aerodynamic diameter dc = Characteristic length (fiber diameter or wire diameter or hole diameter) des = Effective slack length df = Fiber diameter dp = Particle diameter dm = Diameter of the droplets measured under the microscope dw = Wire diameter dh = Hole diameter E = Total efficiency f = Flattening factor to account for distortion of a droplet on a microscope slide FD = Drag force on the particle fOA = Fraction of the projected open area Fr = Froude number g or gi = Gravitational acceleration G = Dimensionless number that controls deposition due to gravitational settling

xx

OAfG = Correction factor h = Height or height of channel H = Correction factor J = Diffusion flux Ko = Darcy’s constant K or Ku = Kuwabara’s hydrodynamic factor L = Filter thickness in the direction normal to the flow l = The length of all the fibers in the unit volume of the filter M = Mesh size mf = Mass of fluorescein collected on the filter or screen n = The number concentration of particles entering the element no = Particle concentration upstream of the filter mat OL = Opening length P = Penetration PISO = Pressure Implicit with Splitting of Operations Ps = Static pressure Q = Corrected volumetric air flow rate R = Interception parameter (Ratio of particle diameter to fiber or wire diameter) RC = Concentric boundary of radius Rf = Radius of a fiberRe = Reynolds number ReC = Reynolds number based on the characteristic length (wire diameter or effective slack length) and the average velocity inside screen ReC,f = Reynolds number based on the characteristic length and the face velocity Ref = Fiber Reynolds number based on the average velocity inside filter Rep = Particle Reynolds number R2 = R-sdquare, Sum Squared error SM = Mesh-Screen Stk = Stokes number or inertia parameter Stkc = Critical Stokes number SIMPLE = Semi-Implicit Method for Pressure-Linked Equation SIMPLEC = Semi-Implicit Method for Pressure-Linked Equation Consistent SSE = Sum of square error t = Time or sampling time th = thickness

xxi

u or Uo = Face velocity, free stream velocity U = Average velocity inside a filter or screen ui = Flow velocity in the ith direction uj = Flow velocity in the jth direction uu = Gas velocity uv = Particle velocity V = Volume of solution used to elute the tracer VTS = Settling velocity of the particle wd = Width wi = Uncertainty of Xi

iRw = Overall uncertainty of Y by all Xi

WL = Wall loss Xi = Measured variables xi = Independent variables in the ith direction xj = Independent variables in the jth direction xv = Particle trajectory x0, x1, x2, x3= Constants Y = Result z0, z1, z2, z3, z4, z5, z6 = Constants α = Solidity or packing density αA = Area solidity δ = Variation η = Single fiber efficiency ηA = Actual efficiency ηI = Single fiber efficiency due to impaction ηIR = The combined single fiber efficiency due to interception and impaction ηSS = Standardized screen efficiency ηSS,corr = Standardized screen efficiency of final correlation ηSS,i = Standardized screen efficiency for each screen ηR = Single fiber efficiency due to interception θ = Angle of staggered type perforated-sheet ρ= Gas density ρa = Air density ρp = Droplet density ρw = Density of water

xxii

λ = Mean free path µ = air viscosity

1

CHAPTER I

INTRODUCTION

Background

Aerosol measurement frequently requires that a sample be conveyed to a

diagnostic device or collection system. For accurate measurements, a representative

aerosol sample must be drawn through an inlet into the particle measuring or collecting

device (Figure 1.1). However, the air sample aspirated into the inlet may be contaminated

with unwanted large-sized debris such as insects, plant debris, and fibers. Such

contaminants are usually removed by a screen placed downstream of the inlet aspiration

region. An effective screen is one that filters the contaminant while allowing aerosol

particles of interest to penetrate with minimum deposition.

Figure 1.1. Representative inlet samplers with screen.

___________

This dissertation follows the style and format of Journal of Aerosol Science.

2

There are several types of commercially available screens that can be classified

based on the fabrication methods and configuration, e.g., electroformed-wire, woven-wire,

welded-wire, perforated-sheet, etc. (Table 1.1). Wire screens are extensively used in an

incredibly wide variety of industries. Its presence is rarely detected as, more often than

not, it is incorporated as a filter or screening medium within a finished product or piece

of equipment. It is used in typical process plants for size classification, product separation,

impurity removal, particle filtration, and mist elimination (Capps, 1994). Woven-wire

and welded-wire screens are the most widely used configurations for commercial sorting,

screening, and filtering applications. Electroformed-wires are used increasingly for small-

scale production of specialty materials and precision quality control. Perforated metal

sheets have been used for a variety of other applications such as sorting, separating,

machine guards, ventilating grills, and fabricating custom parts.

Woven-wire screens can be further classified into different grades such as

standard filter, milling, bolting, strainer, etc. The typical mesh screen is made of wires of

a particular diameter interwoven together to form a perforated planar structure with

desirable mesh openings (shape and size). Depending on the intended application, the

wire size and mesh openings of a screen may vary from a few tens of micrometers to

millimeters. The woven structure of the wire screen may be soft and flexible or as rigid

and durable as a solid steel plate (Soar, 1991). Among woven-wire cloths, bolting grade

has the smallest wire diameter and highest percentage of open area, which suggests that it

should find application in air sampling for blocking the passage of insects while

minimizing loss of particles that are to be sampled.

3

Table 1.1. General information of wire and perforated-sheet screens.

Type Percentage of Wire Diameter Thickness Material Type Grade* PatternOpen Area Range Range Opening

Inch Inch(Micrometers) (Micrometers)

Electroformed Wire Cloth 36.0-98.0 0.0002 - 0.0067 N/A Copper, Gold, Nickel N/A N/A

(5 - 170)

Woven wire cloth 11.7-85.7 0.00079-0.375 N/A Aluminum, Brass, Bronze, Standard, Bolting, N/A

(20 - 9525 ) Copper, Nickel, Silver, Milling, Filter,

Steel Stainless, Steel, Space Cloth,

Titanium Strainer

Welded Wire Cloth 73.6-87.8 0.017 - 0.106 N/A Stainless Steel, Steel N/A N/A

(432 - 2692)

Round Hole Perforated Sheet 10.0-63.0 N/A 0.006 - 0.25 Aluminum, Brass, Plastic, Stainless Steel, Steel N/A Staggered,

Straight

(152 - 6350)

*Standard: Most commonly used grade. Ideal for liquid particle separation, gravel sizing, support screens, basket liners. Bolting: Smaller wire diameter and higher percentage of open area than milling and standard grade. Use for accurate wet and dry sifting and separating. Milling: Smaller wire diameter and higher percentage of open area than standard grade. More durable in processing and sifting applications than standard and bolting grade cloths.

Filter: Tightly woven-wires for very durable, strong mesh. Use for accurate filtration at high pressure and flow rates. Space cloth: Woven from large wire diameters with large, square openings. Strainer: Very fine wire diameter and small mesh size. Good for straining liquids and grading powders.

4

Owing to its great practical importance, the penetration of aerosol particles

through fibrous filters has been widely studied from both the theoretical and experimental

points of view (Fuchs, 1964; Happel, 1959; Kuwabara, 1959; Landahl and Herrman,

1949; Langmuir, 1942; Lee and Liu, 1982; Liu and Pui, 1975; Stechkina and Fuchs,

1966; Stechkina et al., 1969; Suneja and Lee, 1974; Torgeson, 1964). However, for

screens, aerosol penetration studies have been largely confined to the nanoparticles

regime with emphasis on the size separation of these particles using diffusion batteries

that consist of a series of screens (Scheibel and Porstendorfer, 1984; Cheng et al., 1990;

Alonso et al., 2001). Cheng (1993) studied the operating principle, theory, design and

applications, and data analysis of the diffusion batteries.

Collection of uncharged particles by screens is influenced by different particle

deposition mechanisms such as Brownian motion, interception, and inertial impaction.

For a particular screen configuration, flow conditions and particle sizes determine the

mechanisms that govern deposition. The penetration process is strongly influenced by the

mesh size, flow field, and Stokes number (the ratio of the stopping distance of a particle

to a characteristic dimension of the obstacle). A detailed discussion on the deposition

mechanisms for aerosol particles on screen media will be presented later.

Objectives of the Present Study

The principal objective of the present research was to study aerosol deposition on

different types of screens (electroformed-wire, woven-wire, welded-wire, and perforated-

sheet screens) using both experimental and numerical techniques, as a means of

developing models and data that will allow users to predict aerosol deposition on screens.

5

The experimental investigation involved measurements of aerosol losses for different

screen designs and operational conditions. Tests were carried out for screens in the flow

regime (1< ReC <500). Three-dimensional Computational Fluid Dynamics (CFD)

simulations of the experiments were undertaken simultaneously to validate the numerical

approach against experimental data. An additional goal is to develop empirical

correlations summarizing the deposition process on screens and a new parameter that

consolidates aerosol deposition data on screens. The following steps were taken to fulfill

the goals of this project.

Electroformed-Wire Screen was used as a reference screen in the present study.

The primary reason that an electroformed-wire was selected to study aerosol deposition

as a reference wire screen was the fact that openings of precision electroformed-wires are

consistently accurate, in contrast to ordinary wire screens. An experimental technique for

measuring the collection efficiencies (actual efficiency, ηA) and pressure drop through the

screen was developed. A three-dimensional numerical study was performed using

commercial software (Fluent) with electroformed-wire cloth. The numerical results were

compared with the experimental results. An empirical correlation for the actual efficiency

(ηA), as a function of the non-dimension parameters (Stokes number and area solidity),

was then obtained using a multi-variable regression technique. Further, as there is well-

established correlation between the collection efficiency and the non-dimensional

parameters (interception parameter, Reynolds number, and Stokes number) for the

fibrous filtration process, a similar approach was attempted in the process of

standardizing the collection efficiency data on the screens. A model was developed that

will allow users to predict, on an a priori basis, the deposition of aerosol on screens. The

6

entire study can be divided into two primary components: the experimental study and the

numerical study. Both aspects of the study are described in more detail in the following

sections.

Layout and Key Points in Each Chapter

The study reported in this thesis involved a series of different procedures. These

procedures include (a) A review of the previous studies of filtration with fibrous filters,

(b) objective and description of screens, (c) the development of experimental methods,

(d) the conduction of a series of experiments, (e) the development of numerical models,

and (f) development of empirical correlation using a multi-variable regression technique.

Chapter II begins with a description of the review of the previous studies on

aerosol filtration with fibrous filters. Theoretical concepts pertaining to the aerosol

filtrations process are briefly reviewed. A basic introduction of the single fiber concept is

provided. Important deposition mechanisms that influence the transport and deposition of

aerosol particles are outlined. Concepts related to flow and pressure drop across the filter

are provided. Contributions of previous researchers on the filtration process are

summarized.

In Chapter III, a brief description of the different commercially available screen

types are presented and illustrated with sample photographs. Important geometrical

features that characterize each type of screen are outlined. Technical terminology that is

adopted to specify screen characteristics are introduced and are described in detail.

In Chapter IV, various components of the experimental setup used in the aerosol

deposition studies are described in detail. A brief outline of the experimental

7

methodology adopted in the process of conducting tests with liquid aerosols is presented.

Various other issues that are important from the experimental viewpoint in the process of

conducting the studies are introduced and discussed. Finally, details of the experiments

performed on different screen types are provided.

In Chapter V, numerical methodology adopted in the current study is outlined.

Concepts that form the theoretical basis of the numerical approach are briefly presented.

Efforts undertaken to arrive at the appropriate model for the numerical studies are

delineated and the findings are reported. The numerical approach is validated by

providing a comparison of the simulation predictions to experimental data for two

different electroformed wire screens. Further, mention is made of the various simulations

performed on the different screen types.

As a next step, in Chapter VI, simulation predictions for the different screen types

are compared to the corresponding experimental results. This is followed by the

development of empirical correlation equations describing results for each screen type,

utilizing a multi-variable regression technique that enables the user to characterize actual

efficiency using mathematical equations. Details on the development of a methodology to

standardize experimental and numerical results on each screen type are presented. Finally,

non-dimensional groups that influence the screen performance are identified and

correlations expressing the standardized performance as a function of the non-

dimensional groups are evolved.

Chapter VII summarizes the conclusions of the present work and presents a series

of recommendations for future studies. There is a good chance that this work will benefit

screen applications and provide users with a better understanding the deposition process

8

with liquid aerosols. Results of this work may also be used to help individuals in

selecting the appropriate type of screens to remove larger debris while collecting liquid

aerosols with minimum losses.

9

CHAPTER II

THEORETICAL BACKGROUND

Three elements are fundamental in the filtration process are the dispersed aerosol,

the transport medium (usually air), and the porous media, filter or screen. Each of these

elements plays an important role in determining the collection efficiency and pressure

drop. The first step in the process of formulating a quantitative basis for the filtration

phenomenon is an understanding of the flow field and the associated particle behavior at

the single element level. In the case of a fibrous filter, the medium may ideally be

assumed to be composed of a number of cylindrical elements in series and parallel

combinations. Different filter models have been proposed and the flow field

corresponding to each model has been determined. The most important and frequently

used models are an isolated cylinder model (Lamb, 1932), a cell model (Kuwabara, 1959;

Happel, 1959), a fan model (Kirsch and Fuchs, 1968), and a staggered-array-model (Yeh,

1972).

Description of the Filter Models for the Flow Field

The Lamb equation which is frequently used to describe the flow field around an

isolated cylinder has an approximate solution to the Navier-Stokes equation. The isolated

cylinder model ignored the effects of neighboring fibers and packing density, therefore

this model does not represent a realistic flow condition around a cylindrical fiber;

10

nevertheless, Lamb’s theory is accurate at low Reynolds numbers (Re, a dimensionless

number that characterizes fluid flow around an obstacle such as a filter).

The cell model derived by Kuwabara (1959) and Happel (1959) considers the

effect of the neighboring fibers and fiber packing density. This model is based on a firm

theoretical basis and approximates the true flow field in a real filter better than the other

models. The model consists of a fiber of radius (Rf) surrounded by a concentric boundary

of radius (RC) with a packing density, α, that is equal to the ratio of Rf2/RC

2. A zero

gradient of the circumferential velocity was assumed by Happel on the outer boundary of

the cell, whereas, zero vorticity was assumed by Kuwabara. The solution of the

Kuwabara model was obtained based on the assumption that the inertia force term in

Navier-Stokes equations is negligible. Therefore, the solution of this model which was

obtained by ignoring the inertia term in Navier-Stokes equations is valid for creep flow

only.

The fan model which is derived by Kirsch and Fuchs (1968) consists of a series of

layers of equidistant, parallel fibers, which is not so in real filters. To account for this

feature, they introduced an inhomogeneity factor in their model. At the end of the 1960’s,

Fuchs and his co-workers had the conclusion that it is possible to calculate the resistance

and efficiency with sufficient accuracy for practical purposes, if the geometric parameters

(fiber radius, solidity, and filter thickness) are known.

Yeh (1972) selected the staggered-array model which is an approximation of the

fiber structure in a real filter. Fibers in a filter were distributed as a staggered array of

infinitely long parallel cylinders perpendicular to the flow. There is an implicit

assumption that the flow fields around each cylinder are similar (like a periodic boundary

11

condition). Therefore, only the flow field in the region within a rectangular shaped

parallel channel is considered. More importantly, the flow field obtained by solving the

complete form of the Navier-Stokes equations in this model is valid for higher Reynolds

number flows.

In the case of wire screens, few investigators only modeled the pressure drop and

fluid flow through a wire screen regenerator. Cheng et al. (1985) measured the pressure

drop across layers of screens, estimated the single-fiber collection efficiency of screens

and compared his results to the theoretical prediction obtained from fan model filtration.

Yarbrough et al. (2004) investigated three types of models under steady and

oscillating flow conditions; a three-dimensional model of plain woven wire screens, a

two-dimensional staggered tube bank model, and a porous media regenerator model were

built. Their goal was to determine the best model for a wire screen regenerator using the

CFD approach. The plain square weave wire screen model was created initially with one

layer of screen. However, two and three screen models were made (as the copy of the

first screen and positioned behind) since regenerators contain hundreds of screens. Their

results showed that the most realistic model among three different models is the wire

screen model, but it has some requirements (computational size and requirements) for

numerical simulations. The other two models (two-dimensional staggered tube bank

model and porous media model) have to be considered as simplified regenerator models.

The porous media model is the most promising model for simulations, and would also be

the easiest to incorporate into a system level model. However, it does not represent the

flow behavior well.

12

Single Fiber Efficiency Concept

The starting point in studying aerosol penetration through screens is to consider

the capture of particles by a single element of an electroformed-wire, woven-wire,

welded-wire, or perforated-sheet. The classical filtration theory only dealt with isolated

fiber, but the modern filtration theory, single fiber theory, takes into account in the effects

of neighboring fibers. The Reynolds number, Ref that characterizes the flow around a

fiber having a diameter, df , was defined as

µUdρ

Re faf = (2-1)

Where ρa is air density; U is the average velocity inside a filter, Uo/(1-α); df is the fiber

diameter; µ is air viscosity. Uo is called the face velocity, just before the air enters inside

a filter. Let α be the solidity or packing density, i.e., volume fraction of the fibers in the

filter, and l be the length of all the fibers in the unit volume of the filter.

The single fiber efficiency, η, is defined as the ratio of the number of particles

striking the fiber to the number which would strike if the streamlines were not diverted

around the fiber.

The total efficiency, E, of a filter composed of many such individual fibers in a

mat can be related to the single fiber efficiency, η. The solidity and the total efficiency

can be written as

l4

πdα

2f= (2-2)

⎥⎥⎦

⎤

⎢⎢⎣

⎡

−−

−=−=fO d

LnnE

)1(4exp11απηα (2-3)

13

Where n is the number concentration of particles entering the element; no is the particle

concentration upstream of the filter mat; L is the filter thickness in the direction normal to

the flow, and df is the fiber diameter.

The advantage of using the single fiber efficiency is that it is independent of the

filter thickness, L. This is an important point to consider in comparing filters, because a

filter with lower single fiber efficiency can be made to have a higher total efficiency by

simply using more material in the mat.

In real filters, not all of the fibers are placed transverse to the flow. Some fibers

are clumped together, resulting in non-uniform distribution in the filter that will usually

result in a reduced efficiency. In considering the performance of real filters, it is

necessary to take this into account.

Capture Mechanisms

As air flows around a wire, trajectories of particles may deviate from the

streamlines due to several mechanisms. As a result, particles may collide with the fibers

or wires and deposit on them. The important deposition mechanisms for particles in the

size range of interest (2 to 20 µm AD) are inertial impaction, interception, and

gravitational settling (Hinds, 1998). Other mechanisms such as electrostatic and diffusion

were ignored in this study because diffusion is only dominated for particle below

submicron size range and the electrostatic effects are pre-eliminated before test.

Even if the trajectory of a particle does not depart from the original streamline, a

particle may still be collected if the streamline brings the particle center to within one

particle radius from the fiber surface, which is called the interception effect. One would

14

expect the interception to be relatively independent of flow velocity for a given filter

(Figure 2.1), which can be contrasted to the flow dependent characteristics of diffusion

and inertial impaction. The dimensionless parameter describing the interception effect is

the interception parameter (R), defined as the ratio of particle diameter to fiber or wire

diameter.

Fluid streamlines around a cylinder are curved. Particles with a finite mass

moving with the flow may deviate from streamlines due to their inertia (Figure 2.1). If

the curvature of a streamline is sufficiently large and the mass of a particle sufficiently

high, the particle may deviate far enough to collide with the cylinder. The importance of

this inertial impaction mechanism increases with increasing particle size and increasing

air velocity. This is contrary to that for diffusion, where both smaller size and lower

velocity increase the opportunity of collision of particles with cylinders. By the Stokes

number, the mechanism of inertial impaction is defined as:

c

o2

ppc

d18µUdρC

Stk = (2-4)

Where Cc is Cunningham’s slip correction; ρp is the particle density; dp is the particle

diameter; Uo is the face velocity; µ is the gas viscosity; and dc is the characteristic length

(fiber diameter, wire diameter or slack width). The Stokes number is the basic parameter

describing the inertial impaction mechanism for particle collection in a filter or a wire. A

large Stokes number implies a high probability of collection by impaction, whereas a

small Stokes number indicates a low probability of collection by impaction.

15

(a) Interception

(b) Impaction

Figure 2.1. Illustration of particle collection by a single fiber or wire through the interception and impaction mechanisms.

With a finite velocity, particles will settle with a finite velocity in a gravitational

force field. When the settling velocity is large enough, particles may deviate from the

streamline. This mechanism is typically important for particles larger than at least a few

micrometers in diameter and at low velocities. The dimensionless number that controls

deposition due to gravitational settling is the parameter G.

In this research, aerosol deposition on the screen was not represented as being

caused by a combination of the individual efficiencies (as in the single fiber concept), but

the overall efficiency value was estimated.

In some filtration theories, it is assumed that the individual filtration mechanisms

discussed above are independent of each other and additive. Therefore, η, the overall

single fiber collection efficiency in Equation 2-2, can be written as the sum of individual

single filter efficiencies contributed by the different mechanisms. This approximation has

been found to serve adequately for predicting the overall collection efficiencies, owing to

the different ranges in particle sizes and face velocities in which different filtration

mechanisms predominate (Hinds, 1998). Some theories combine interception with

diffusion or inertial impaction to provide more realistic models. Sometimes a small

correction term is included to take into account the combined effect. Additionally, the

wake region behind the wires could introduce some minor collection. The amount

collected is dependent on the Reynolds number.

Where Uo is the face velocity; VTS is the settling velocity of the particle; and, g is the

gravitational acceleration. Generally, effect of gravitational settling is small compared to

other mechanisms considered in this study; unless the particle size is large and the face

velocity is low, this mechanism should be unimportant.

Summary of Earlier Researchers’ Results

Theoretical and numerical results are summarized in Tables 2.1 to 2.3. The first

systematic study of aerosol filtration, by mats of cylindrical fibers, was made by

16

o

cpp

o

TS

UgCd

UVG

µρ

18

2

== (2-5)

Table 2.1. Single fiber efficiency due to interception mechanism.

Investigator Equation for Interception, ηR Remarks

Langmuir (1942) ⎥⎦

⎤⎢⎣

⎡+

++−++−

=)1(

1)1()1ln()1(2))ln(2(2

1R

RRRReRη Lamb’s Flow (1932)

Friedlander (1957) O

R KR

225.1 82.1

=η where ReKO ln0022.2 −= Tomotika & Aoi Flow (1951)

Kuwabara (1959) ⎥⎦⎤

⎢⎣⎡ +−−

+++−+

+= 22 )1(

2)

21()

11(1)1ln(2

2)1( R

RR

KR

Rαααη

where 43

41ln

21 2 −−+−= αααK

Natanson (1962) 21 RKO

R =η where ReKO ln0022.2 −= Lamb’s flow for R<<1

Torgeson (1964) 23

ln240518.0 R

ReR −=

πη Lamb’s Flow

Fuchs (1964) )1(11

RRR +−+=η Potential Flow

Stechkina and Fuchs (1966) ⎥

⎦

⎤⎢⎣

⎡+

+−++

= 2)1(11)1ln(2

2)1(

RR

KRαη

Lee and Ramamurthi (1993) )1(

)1( 2

RR

KR +−

=αη for 0.005<α<0.2

17

Table 2.2. Single fiber efficiency due to inertial impaction mechanism.

Investigator Equation for Inertial Impaction, ηI Remarks

Landahl & Herrmann (1949) 22.077.0 23

3

++=

StkStkStk

Iη Re=10

Yeh and Liu (1974a)

2)2()(

KJStk

I =η

8.2262.0 5.27)286.29( RRJ −−= α for R<0.4 0.2=J for R>0.4

2

41

43ln

21 ααα −−+−=K

for 0.005<α<0.2, 0.1<df<50µm and Re<1

Schweers et al. (1994)

)1(10

2.3)(56.28.0

RStk

RReLogStk

StkI +⎟⎟

⎠

⎞⎜⎜⎝

⎛ −−−

+=η for 1<Re<60

18

19

Table 2.3. Single fiber efficiency due to interception plus inertial impaction mechanisms.

Investigator Equation for Interception Plus Inertial Impaction, ηIR Remarks

Davies (1952) [ ]21052.0)8.05.0(16.0 RStkStkRRIR −++=η for Re=0.2

Torgeson (1964) ⎥⎦

⎤⎢⎣

⎡++=

−)8.05.0(1 2

3

RStkRRIR ηη Where Rη from Table 2

Stechkina et al. (1969)

IRIR ηηη +=

where 22 )K(StkJ

I⋅

=η

⎥⎦

⎤⎢⎣

⎡+

++−++=)1(

1)1()1ln()1(221

RRRR

KRη

822620 52728629 .. R.R).(J −−= α

43

41ln

21 2 −−+−= αααK

For Stk<<1

Suneja and Lee (1974)

StkR

Stk

IR 32

)Re(ln0167.0Reln23.053.11

122+

⎥⎦

⎤⎢⎣

⎡ +−+

=η for Re<500

20

Langmuir (1942). Landahl and Herrmann (1949) employed the flow field in calculating

the inertial impaction efficiency and gave an equation for Re = 10. Davies (1952) was the

first to calculate the filtration efficiency due to interception and inertial impaction by the

use of viscous flow. His calculation was presented in a graphical form for Re = 0.2 and

the equation has been found to fit his results. Improved theories have been developed

using more reliable and exact flow fields. Friedlander (1957), Kuwabara (1959),

Natanson (1962), Fuchs (1964), Stechkina and Fuchs (1966), and Lee and Ramamurthi

(1993) calculated the efficiency due to interception. Torgeson (1964) combined the

filtration efficiencies due to interception and inertial impaction. In addition to the above

investigations, the studies of Lee and Liu (1982), Liu and Pui (1975), Suneja and Lee

(1974), Yeh and Liu (1974a and 1974b), and Schweers et al. (1994) consider efficiency

due to inertial impaction.

Compared to the above literature on aerosol deposition on fibrous filters, aerosol

penetration studies on screens have been largely confined to the nanoparticle regime with

emphasis on size separation of these particles using diffusion batteries that consist of a

series of screens (Scheibel and Porstendorfer, 1984; Cheng and Yeh, 1980; Alonso et al.,

2001). Alonso et al. (2001) presents experimental results of aerosol penetration through a

wire screen for mobility equivalent particle diameters between 2 and 10 nm. His

experimental investigation on the relationship between single fiber efficiency for

diffusional deposition and the Peclet number was carried out for a relatively wide range

of Reynolds numbers and an empirical equation was obtained. There is little information

available on the penetration of aerosol particles in the size range of interest for sampling

inlets, which is generally comprised of sizes less than about 20 µm Aerodynamic

21

Diameter (AD). Studies of aerosol deposition on different types of screens are quite rare

and have not been characterized in detail.

Pressure Drop Across Screens

Prediction of pressure drop is an important part of a filtration study for the simple

reason that the measured pressure drop value can be used to validate the accuracy of the

flow field calculations that are subsequently used for the determination of the aerosol

collection efficiency. In other words, once a flow field is solved numerically, the

corresponding pressure drop can be calculated and compared with the actual

measurements.

Fluid flow in filters is usually viscous at low velocity; therefore, the pressure drop

across the filter is approximately proportional to the flow rate. Darcy (1856) first

described this in his book on water flow through a porous medium. He provided Darcy’s

Law, which is valid only for small Reynolds numbers and for cases where the inertia term

in the Navier-Stokes equation is unimportant. As the velocity increases, the inertia term

in the Navier-Stokes equation is no longer negligible and begins to affect the flow field.

According to Davies (1973), the upper limit for the viscous flow regime occurs at a

Reynolds number of about 0.05 and the inertia is important in the region 0.05 <Re< 20.

Langmuir’s expression for pressure drop is based on a model in which evenly

spaced cylinders are located with their axes parallel to the flow direction (Langmuir,

1942). He stated that the resistance of the filter would be increased by a factor of 1.4

compared to that given by the equation when the cylinders are arranged across the flow

direction. Iberall (1950) took into account the random orientation of the fibers by

22

assuming an equal distribution of fibers in three perpendicular directions. Davies (1952),

using dimensional analysis, correlated his theoretical results with pressure drop data for a

large number of filter media.

There have been studies of the flow through screens, though a considerable

amount of work has been done on the flow of gases and this has been reviewed by Laws

and Livesay (1978). Weighardt (1953) investigated liquid flow and proposed an empirical

correlation for pressure drop as a function of wire diameter, flow rate, and physical

properties of the liquid. Ehrhardt (1983) has extended the work and covered a wider

range of conditions (0.5 ≤ ReC ≤ 1000). Several works have been published about the

porosity and pressure drop at steady flow conditions for wire-mesh woven screens.

Armour and Cannon (1968) investigated several types of screens through experiments

made in a bed with a single screen layer. Correlations to evaluate the porosity, based on

the geometry of the screen, were also proposed. Chang (1990) demonstrated the

importance of the inclusion of the actual thickness of the wire screen for an accurate

estimate. Simon and Seume (1988) provide a further review of friction factor correlations

for steady flow and also presented the compressibility effects and the oscillating

characteristics of the flow. Wakeland and Keolian (2003) presented measurements of the

resistance to oscillating flow for 0.002 ≤ ReC,f ≤ 400 of individual woven-wire screens.

23

CHAPTER III

DESCRIPTION OF SCREENS

The geometry of screens generally varies based on the relative dimensions of the

elements. The most common type is the plain weave type of wires evenly spaced in both

directions. Another simple type in frequent use is represented by the perforated-sheet.

The relative scale of any type is best described by the fraction of open area, the fractional

degree of which the screen obstructs the flow. The range of the fraction of open area is

from zero for no screen to unity for a solid plate. The full range is important, although the

two limits have no practical significance. We refer to each screen by its nominal size in

both units (inch and µm). Tested screen dimensions are found in Table 3.1.

Wire Screen

A plain weave type of wire screen (electroformed-wire, woven-wire, and welded-

wire) was chosen for this study (Figures 3.1 to 3.3). The important screen parameters are

the fraction of open area (fOA), characteristic length (dw), and mesh size (M). The term

mesh refers to the number of openings per unit length. The distance is the length between

the two centers of the adjacent parallel wires, which is simply the inverse of the mesh

number. The clear width of the mesh opening is the distance minus the diameter of the

wire. We calculate the fraction of open area (fOA) of a screen by computing the fraction of

24

Table 3.1. Specification of screens tested for this study.

Screen Grade Opening Fraction of Mesh

Type Pattern Open Area Size(f OA )

inch µm % inch µm inch µm inch µm

1 Electroformed N/A N/A 0.00629 160 56.0 40 N/A N/A 0.01871 4752 Electroformed N/A N/A 0.00268 68 75.0 50 N/A N/A 0.01732 4403 Electroformed N/A N/A 0.00138 35 88.0 45 N/A N/A 0.02080 5284 Electroformed N/A N/A 0.00257 65 90.0 20 N/A N/A 0.04740 1204

1 Woven Standard N/A 0.01700 432 43.6 20 N/A N/A 0.03300 8382 Woven Bolting N/A 0.00450 114 50.7 64 N/A N/A 0.01110 2823 Woven Standard N/A 0.01800 457 50.7 16 N/A N/A 0.04450 11304 Woven Milling N/A 0.00950 241 51.1 30 N/A N/A 0.02380 6055 Woven Milling N/A 0.01600 406 55.4 16 N/A N/A 0.04650 11816 Woven Milling N/A 0.01700 432 58.1 14 N/A N/A 0.05440 13827 Woven Bolting N/A 0.00950 241 71.9 16 N/A N/A 0.05300 1346

1 Welded N/A N/A 0.01700 432 74.6 8 N/A N/A 0.10800 2743

1 Perforated N/A Staggered 0.01500 381 21.0 N/A 0.0310 787 0.014 356 N/A N/A2 Perforated N/A Staggered 0.18750 4763 51.0 N/A 0.2500 6350 0.060 1524 N/A N/A

‡OL: Opening Length

†CS: Center-to-Center Spacing

OL‡Characteristic

Length(dw or d h )

CS† Thickness

(th )

25

Photo (40× magnification) (400× magnification) Photomicrographs

(a) 45×45, 0.00138-inch, 0.88

Photo (40× magnification) (400× magnification) Photomicrographs

(b) 20×20, 0.002565-inch, 0.90

Figure 3.1. Electroformed-wire screen tested. Parameters in each figure are mesh size (M), wire diameter (dw) and fraction of open area (fOA).

the projected open screen area, instead of the volume fraction of the actual cylinder-

shaped wire, as would be the case for a fibrous filter (Figure 3.4). The equation for fOA

can be expressed in this form for each screen,

2)1( Meshdf wOA ×−= (3-1)

It must be noted that even though, in theory, wire screen configurations with a

specific wire size and a mesh opening size could be made, not all of them are

commercially available. For example, screens with small wire diameters and large mesh

openings would have limited value in industrial applications. Therefore, for this study,

26

14×14, 0.017-inch, 0.581 16×16, 0.0095-inch, 0.719

16×16, 0.016-inch, 0.554 16×16, 0.018-inch, 0.507

20×20, 0.017-inch, 0.436 30×30, 0.0095-inch, 0.511

64×64, 0.0045-inch, 0.507

Figure 3.2. Woven-wire screen tested. Parameters in each figure are mesh size (M), wire diameter (dw) and fraction of open area (fOA).

27

8×8, 0.017-inch, 0.746

Figure 3.3. Welded-wire screen tested. Parameters in each figure are mesh size (M), wire diameter (dw) and fraction of open area (fOA).

Figure 3.4. Schematic for the calculation of fraction of open area (fOA) on wire screen.

28

wire screens sample covering a wide range of commercially available wire size and mesh

openings, which could potentially be of use in aerosol sampling apparatus, were selected

for the experiments.

Openings of precision electroformed-wires are consistently accurate in contrast to

ordinary woven-wires. Acceptable tolerances of opening sizes for electroformed-mesh

screens (InterNet Inc., Anoka, MN) are specified in the American Society of Testing and

Materials (ASTM) Standard E-161-00 (ASTM, 2004a). Regardless of opening size, the

allowable tolerance on the range of opening sizes is ± 2 micrometers. The tolerances for

woven-wire are specified by ASTM Standard E-11-04 (ASTM, 2004b), for which a

summary is given in Table 3.2.

Table 3.2. Tolerances for woven-wire and perforated-sheet openings are specified by ASTM Standard E-11-04.

Wire Diameter Tolerance Opening ToleranceLength

inch Micrometers inch MicrometersUnder 0.0048 ± 2.54 1/16 to 1/8 ± 177.8

Under 0.0080 to 0.0048 ± 5.08 Over 1/8 to 3/16 ± 254.0Under 0.0120 to 0.0080 ± 7.62 Over 1/8 to 1/4 ± 304.8Under 0.0024 to 0.0120 ± 10.16 Over 1/4 to 3/8 ± 381.0

Over 3/8 to 1/2 ± 431.8Over 1/2 to 3/4 ± 508.0Over 3/4 to 1 ± 762.0

Perforated-Sheet Screen

Figure 3.5 shows a round-hole perforated sheet screen with a staggered opening

pattern. In general, manufacturer provides the following basic information on the screen:

the fraction of open area (fOA), center-to-center spacing (CS), hole size (dh), thickness (th),

and the angle of the staggered opening pattern. We calculate the fraction of open area

29

0.015-inch, 0.21 0.188-inch, 0.51 Figure 3.5. Perforated-sheet screen tested. Parameters in each figure are hole diameter (dh) and fraction of open area (fOA). (fOA) of a perforated-sheet screen by computing the fraction of the projected open screen

area (Figure 3.6). The equation for fOA can be expressed in the following form:,

2

2

.).()(sin)2/(SC

df h

OA ×=

θπ

(3-2)

Determination of the characteristic dimension (equivalent to the wire diameter for

the other screen types) for perforated-sheet screen is complicated owing to the nature of

the screen and the geometrical structure. It would be seen in the future chapters that the

choice of the characteristic length greatly influences the shape of the collection efficiency

curve. A discussion on the various methodologies examined in the course of the above

research based on suggestions available in literature and the determination of the

characteristic dimension is presented later. The tolerances for perforated-sheet hole

diameter are specified by ASTM Standard E-323-80 (ASTM, 2004c), for which a

summary is given in Table 3.3.

30

Figure 3.6. Schematic for the calculation of fraction of open area (fOA) on perforated-sheet screen.

Table 3.3. Tolerances for hole diameter of perforated-sheet are specified by ASTM Standard E-323-80.

Screen Type Hole Diameter Tolerance

inch MicrometersPerforated Sheet Under 0.0048 ± 2.54

Under 0.0080 to 0.0048 ± 5.08Under 0.0120 to 0.0080 ± 7.62Under 0.0024 to 0.0120 ± 10.16

31

CHAPTER IV

EXPERIMENTAL STUDIES

This chapter describes the experimental setup, procedure, and a screen efficiency

measuring technique based on certain new configuration developments at the Aerosol

Technology Laboratory (ATL). It includes mixing requirements, sampling locations, and

description of measuring apparatus, data processing, experimental parameter, and

methodology.

Detailed experimental studies were conducted on different commercially available

screens to characterize screen deposition. Aerosol particle is generated by the Vibrating

Orifice Aerosol Generator (VOAG) (Berglund and Liu, 1973) and an Aerosol Particle

Sizer (APS, Model 3321, TSI Inc., St. Paul, MN), which enabled particle distribution to

be checked quickly. In this study, only commercial available screens were used. The

Reynolds number, ReC (Subscript C for the characteristic length), as defined previously,

varied between 0.5 and 600 for this study. For wire screens, the obstacle length (wire

diameter) is used as the characteristic length. However, determination of the

characteristic length in the case of perforated sheet screens is more complicated, and is

estimated based on the diameter of an imaginary wire (effective slack length), as

demonstrated in the calculation presented in Appendix-1. The collection efficiency is

obtained as a function of Stokes number.

32

Aerosol Generator

A nearly monodisperse aerosol was generated with a vibrating orifice aerosol

generator from a mixture of non-volatile oleic acid, ethanol, and a fluorescent analytical

tracer (sodium fluorescein). The test aerosol was passed through a 10 mCi Kr-85 source

to neutralize any electrical charge on the aerosol. The particles are thus brought to a state

of Boltzmann charge equilibrium. A mixture of master solution is the combination of 9%

oleic acid and 1% sodium fluorescein salt (uranine) dissolved in 90% ethanol to create

the liquid particle. The interested range of particle size is controlled by diluting the

master solution while maintaining the operational parameters of the VOAG.

Aerosol Size Distribution and Measurement of Aerosol Particle Size

The consistency of aerosol concentration and monodispersity is an important

consideration when generating the aerosol particle. The diameter of the aerosol particles

was determined by collecting a sample on an oil-phobic glass slide and then measuring

the apparent size under a microscope. Aerodynamic diameter, da, of the aerosol particles

is calculated from:

wa

PPma C

Cf

ddρρ

= (4-1)

Here, dm = diameter of the droplets measured under the microscope; f = flattening factor

to account for distortion of a droplet on a microscope slide (Olan-Figueroa et al., 1982);

Cp = Cunningham’s slip correction factor based on the physical particle diameter (dm/f);

ρP = droplet density (934 kg/m3) for a mixture of oleic acid and sodium fluorescein tracer;

Ca = Cunningham’s slip correction factor based on the aerodynamic diameter; and, ρw =

density of water.

33

The value of f is 1.29 (ATL, 2005) for oleic acid/sodium fluorescein mixture

deposited on slides coated with an oil-phobic agent (NYEBAR, Type Q, 2.0%, NYE

Lubricants Inc., New Bedford, MA). During the course of an experiment, the size

distribution of particles output from the VOAG is continuously monitored with an APS.

This equipment is used to provide assurance of a constant particle size throughout the

experiment; however, because of errors of this device in sizing liquid droplets (Baron,

1986), it is not used for characterizing the actual size. The particle size range spanned by

the APS is from 0.5 to 20 µm. Particles are also detected in the 0.3 to 0.5 µm range using

light-scattering.

Experimental Methodology

Figures 4.1 and 4.2 show a photo and a schematic diagram of the system used for

the screen penetration tests. The system is comprised of a Vibrating Orifice Aerosol

Generator (VOAG, Berglund and Liu, 1973), a Kr-85 neutralizer, a vertical tube (147

mm diameter), an Aerosol Particle Sizer (APS, Model 3321, TSI Inc., St. Paul, MN), a

filter holder, and a Hi-Vol blower. The Hi-Vol blower (Model GBM2360,

ThermoAndersen, Smyrna, GA) system was calibrated using a Roots meter (Model 5M

125 TC, Dresser Measurement, Houston, TX), a digital flow meter (HFC-digital-1400,

Hi-Q Env. Products, San Diego, CA), and a U-tube or digital manometer (Model 8360,

TSI Inc., St. Paul, MN).

34

Figure 4.1. Photo of setup for screen test.

35

Kr-85 Neutralizer

Figure 4.2. Schematic of setup for screen test.

Hi-Vol Blower

APS

0.2 m (8 inch) Duct

VOAG

Flow straightener

Mixing box

½D

½D

1.2D

9D

Screen location

Filter holder

0.15 m (5.78 inch) I.D.PVC Pipe

Screen holder for wovenwire, welded wire and

Screen holder for

perforated sheet

O-Ring

Screen

Screen

PVC Pipe

O-Ring

PVC Pipe

electroformed wire

Aluminum holder combined with screws

36

Pressure drop across the screen was measured with a Magnehelic differential

pressure gauge (Dwyer Instruments, Michigan City, IN). A Hi-Vol blower system was

calibrated using a roots meter (full flow ranges; 200-3000 L/min) and H-Q digital meter

(low flow ranges; 200–1500 L/min) with U-tube and digital manometer was shown in

Figure 4.3. The flow rates are continuously monitored with digital pressure meter and

manometer.

Flow Rate, L/min0 500 1000 1500 2000 2500 3000

Pres

sure

, inc

h-H

2O

0

5

10

15

20

25Digital TSI & H-QU-tube w/ Temp Correction

Figure 4.3. Calibration result of Hi-Vol Blower using root meter (full flow ranges; 200-3000 L/min) and H-Q digital meter (low flow ranges; 200–1500 L/min) with U-tube and digital manometer.

The test procedure consists of first placing the screen and filter medium in the

holder, bringing the aerosol generator to a steady operating condition, and then measuring

the particle size distribution generated by the VOAG. The electrically neutralized aerosol

37

is passed through a 0.203 m (8.0 inches) duct into a Generic Tee Plenum (Han et al.,

2005). The characteristic dimensions of the GTPs are 0.305 m × 0.305 m × 0.457 m (12

inches × 12 inches × 18 inches), where the dimensions are scaled to the reference

dimensions of the duct (0.203 m). The GTP mixing system was developed to provide

ANSI/HPS Standard N13.1-1999 compatible sampling locations in short runs of ducts

downstream of the mixing element and operate with a relatively low pressure loss.

Results from these tests show that the mixing is well within the ANSI/HPS

Standard N13.1-1999 criteria – the coefficient of variation (COV) for velocity and tracer

gas were less than the 20% criteria levels at measurement locations (0.7 duct diameters

upstream and 1 duct diameter downstream of the screen location). Velocity

measurements were made with a TSI Inc., thermal anemometer, Model 8360, Serial

Number 505025. Tracer gas tests were conducted by releasing a continuous stream of

dilute sulfur hexafluoride (SF6) at the center of the duct intake (Figure 4.2). Samples

were extracted at the sampling location with 60 mL hypodermic syringes from the 4-

points of each traverse location for the flow rate of 1080 L/min. The samples were

analyzed with a gas chromatograph (Lagus Model 101 Autotrac, Serial Number 140,

Lagus Applied Technology, Inc., San Diego, CA).

The detailed flow disturbance velocity measurements and turbulent intensities

was provided at the sampling location, which were produced by using a TSI Inc., hot wire

anemometer, Model 157 (Table 4.1 and Figures 4.4 to 4.9). Measurements for

characterizing the COVs of velocity with and without screens were made at the sampling

locations. Tests were conducted at a particular flow condition, about 1200 L/min.

Velocity measurements were made at the center 7-points of each traverse location. Next,

38

Table 4.1. The summary of average velocity and COV at each configuration.

u AVG Std. Dev. AVG COV(m/s)

Without screenUpstream 1.62 0.26 16.10

Downstream 1.62 0.14 8.70With screen

16×16 Mesh, 0.018-inch, 51%Upstream 1.59 0.23 14.20

Downstream 1.64 0.08 5.0020×20 Mesh, 0.017-inch, 44%

Upstream 1.62 0.29 17.80Downstream 1.60 0.06 3.40

Configuration and Location

the data collected at each traverse point were normalized to the mean velocity of the set.

The COV was then computed from the standard deviation of the normalized velocity

values at each point. The average COV was then computed from the COVs of each test.

Table 4.1 shows the COVs of velocity concentrations for the two different screens at

measurement locations 0.5-duct diameter upstream and 1.0-duct diameter downstream of

the screen location. The screen produced COVs of less than 18.0% for the velocity

concentration at 0.5 duct diameters upstream and less than 5.0% for 1.0 duct diameter

downstream. From these velocity results obtained in the present study, the use of GTP

downstream of the interface of the system appears to affect the good mixing performance

for aerosol deposition on screens.

The flow is drawn through a 0.147 m (5.78 inches) diameter vertical pipe, then

through a glass fiber filter, and exhausted from the system. A Hi-Vol blower and voltage

meter arrangement with a flow controller was used to suck air from the system. The

conditions of the tests for this study are presented in Table 4.2, which are shown as

particle size, flow rates, flow Reynolds number, characteristic length Reynolds number,

39

Normalized radial distance-1.0 -0.5 0.0 0.5 1.0

0.0

0.5

1.0

1.5

2.0Traverse P1Traverse P2

Nor

mal

ized

vel

ocity

(a) Normalized velocity profile

Normalized radial distance-1.0 -0.5 0.0 0.5 1.0

Turb

ulen

t int

ensi

ty, %

0

5

10

15

20

25

30Traverse P1Traverse P2

(b) Turbulent intensity profile

Figure 4.4. Normalized velocity profile and turbulent intensity at 0.7-duct diameter upstream of screen location. uAVG = 1.62 m/s, Std. Dev.AVG = 0.261, COV = 16.1%.

40

Normalized radial distance-1.0 -0.5 0.0 0.5 1.0

0.0

0.5

1.0

1.5

2.0Traverse P1Traverse P2

Nor

mal

ized

vel

ocity

(a) Normalized velocity profile

Normalized radial distance-1.0 -0.5 0.0 0.5 1.0

Turb

ulen

t int

ensi

ty, %

0

5

10

15

20

25

30Traverse P1Traverse P2

(b) Turbulent intensity profile

Figure 4.5. Normalized velocity profile and turbulent intensity at 1.0-duct diameter downstream of screen location. uAVG = 1.62 m/s, Std. Dev.AVG = 0.141, COV = 8.7%.

41

Normalized radial distance-1.0 -0.5 0.0 0.5 1.0

0.0

0.5

1.0

1.5

2.0Traverse P1Traverse P2

Nor

mal

ized

vel

ocity

(a) Normalized velocity profile

Normalized radial distance-1.0 -0.5 0.0 0.5 1.0

Turb

ulen

t int

ensi

ty, %

0

5

10

15

20

25

30Traverse P1Traverse P2

(b) Turbulent intensity profile

Figure 4.6. Normalized velocity profile and turbulent intensity at 0.7-duct diameter upstream of screen location with screen (16×16 Mesh, 0.018-inch, 0.51). uAVG = 1.59 m/s, Std. Dev.AVG = 0.225, COV = 14.2%.

42

Normalized radial distance-1.0 -0.5 0.0 0.5 1.0

0.0

0.5

1.0

1.5

2.0Traverse P1Traverse P2

Nor

mal

ized

vel

ocity

(a) Normalized velocity profile

Normalized radial distance-1.0 -0.5 0.0 0.5 1.0

Turb

ulen

t int

ensi

ty, %

0

5

10

15

20

25

30Traverse P1Traverse P2

(b) Turbulent intensity profile

Figure 4.7. Normalized velocity profile and turbulent intensity at 1.0-duct diameter downstream of screen location with screen (16×16 Mesh, 0.018-inch, 0.51). uAVG = 1.64 m/s, Std. Dev.AVG = 0.082, COV = 5.0%

43

Normalized radial distance-1.0 -0.5 0.0 0.5 1.0

0.0

0.5

1.0

1.5

2.0Traverse P1Traverse P2

Nor

mal

ized

vel

ocity

(a) Normalized velocity profile

Normalized radial distance-1.0 -0.5 0.0 0.5 1.0

Turb

ulen

t int

ensi

ty, %

0

5

10

15

20

25

30Traverse P1Traverse P2

(b) Turbulent intensity profile

Figure 4.8. Normalized velocity profile and turbulent intensity at 0.7-duct diameter upstream of screen location with screen (20×20 Mesh, 0.017-inch, 0.44). uAVG = 1.62 m/s, Std. Dev.AVG = 0.288, COV = 17.8%

44

Normalized radial distance-1.0 -0.5 0.0 0.5 1.0

0.0

0.5

1.0

1.5

2.0Traverse P1Traverse P2

Nor

mal

ized

vel

ocity

(a) Normalized velocity profile

Normalized radial distance-1.0 -0.5 0.0 0.5 1.0

Turb

ulen

t int

ensi

ty, %

0

5

10

15

20

25

30Traverse P1Traverse P2

(b) Turbulent intensity profile

Figure 4.9. Normalized velocity profile and turbulent intensity at 1.0-duct diameter downstream of screen location with screen (20×20 Mesh, 0.017-inch, 0.44). uAVG = 1.60 m/s, Std. Dev.AVG = 0.055, COV = 3.4%

45

Table 4.2. Operation condition of experiment for each screen.

Screen Fraction of Mesh Particle Q Re Re C R StkType Open Area Size size

(f OA ) (M) AD Min-Max Min-Max Min-Max Min-Max Min-Maxinch µm % µm L/min

1 Electroformed 0.00629 160 56.0 40 N/A N/A N/A N/A N/A N/A2 Electroformed 0.00268 68 75.0 50 N/A N/A N/A N/A N/A N/A3 Electroformed 0.00138 35 88.0 45 4-20 196-1962 1839-18411 0.5-5 0.122-0.559 0.63-14.764 Electroformed 0.00257 65 90.0 20 4-20 108-1080 1013-10135 0.5-5 0.066-0.301 0.56-19.02

4-20 108-1962 1013-18411 0.5-5 0.066-0.559 0.56-19.02

1 Woven 0.0170 432 43.6 20 3-20 300-2500 2815-23460 19-158 0.007-0.047 0.10-6.922 Woven 0.0045 114 50.7 64 10-17 109-2356 1026-22108 2-34 0.089-0.152 0.30-7.913 Woven 0.0180 457 50.7 16 3-20 100-2500 2815-23460 17-144 0.007-0.045 0.09-6.534 Woven 0.0095 241 51.1 30 10-20 150-2356 1408-22108 5-71 0.042-0.083 0.20-7.465 Woven 0.0160 406 55.4 16 3-20 300-2500 2815-23460 14-117 0.007-0.050 0.10-7.356 Woven 0.0170 432 58.1 14 3-20 250-2500 2347-22437 12-119 0.007-0.047 0.10-6.927 Woven 0.0095 241 71.9 16 3-20 112-2500 1051-23460 2-54 0.012-0.083 0.23-7.60

3-20 80-2500 751-23460 1-268 0.007-0.152 0.08-8.36

1 Welded 0.0170 432 74.6 8 3-20 300-2500 2815-23460 11-93 0.007-0.047 0.13-6.92

1 Perforated 0.0150 381 21.0 N/A 7-20 210-2620 1971-24586 27-340 0.016-0.047 0.17-6.932 Perforated 0.1875 4763 51.0 N/A 11-20 550-2500 5161-23460 126-573 0.006-0.011 0.11-1.63

7-20 210-2500 1971-24586 27-573 0.006-0.047 0.11-6.93

3-20 80-2500 751-24586 0.5-573 0.0067-0.559 0.08-19.02

Wire diameterHole diameter

(dw or d h )

*Note: Grey highlight is for the overall ranges for each screen.

46

interception parameter and Stokes number ranges. Samples obtained through the screen

are collected on 8 inches × 10 inches rectangular sheet filters (Part No. FP2063-810,

Borosilicate Glass Fiber, HI-Q Environmental Products Co., San Diego, CA). Each

screen with the dimension of 0.157 m (6.17 inches) diameter was positioned horizontally

at a distance of 1.2-duct diameters below the flow straightener.

The system was operated with after-filter (AF) placed downstream of mesh-screen

(SM). A solution of 2/3 (200 mL) isopropyl alcohol and 1/3 (100 mL) distilled water was

used to elute the sodium fluorescein from the collection filter and to wash it from the

screens. One drop of sodium hydroxide (1N) is added to the solution in order to stabilize

the fluorescein, which is then analyzed with a digital fluorometer (Model 450, Sequoia-

Turner Corp., Mountain View, CA). The relative aerosol concentration, C, is calculated

from:

tQVc

C f

⋅

⋅= (4-2)

Here, cf = concentration of fluorescein in filter or screen sample (fluorometer reading); V

= volume of solution used to elute the tracer; Q = corrected air flow rate; and, t =

sampling time. The actual efficiency of the screen, ηA, can be expressed as:

AFSM

SMA CC

C+

=η (4-3)

The aerosol penetration through a screen, P, is:

AP η−=1 (4-4)

Wall losses between the screen holder and filter holder (Figure 4.10) were measured to be

about 0.3% to 6%, in the range of flow Reynolds number (Re), 500 to 20000.

47

i

o

CC−

= iCLoss Wall

Reynolds number, Re0 5000 10000 15000 2000

Wal

l los

s

0.001

0.01

0.1

Figure 4.10. Wall losses between screen holder and filter holder.

Table 4.3. Minimum and maximum wall losses for each screen.

.

Screen Wire/Hole Diameter Areal Mesh

inch Porosity Size Min MaxElectroformed 0.00257 0.90 20 0.52% 2.45%

0.00138 0.88 45 0.69% 4.34%Woven 0.014 0.21 40 0.91% 5.56%

0.017 0.44 20 0.89% 5.56%0.005 0.51 64 0.53% 5.23%0.018 0.51 16 0.89% 5.56%0.010 0.51 30 0.60% 5.23%0.016 0.55 16 0.89% 5.56%0.017 0.58 14 0.79% 5.56%0.010 0.72 16 0.32% 5.56%

Welded 0.017 0.75 8 0.89% 5.56%Perforated 0.016 0.21 N/A 0.72% 5.84%

0.063 0.51 N/A 1.38% 5.56%

Wall Loss

48

An appropriate correlation was developed based on the above data (Figure 4.10) and used

to correct the actual efficiency value calculate for each data point (Table 4.3). Therefore,

the actual efficiency of the screen, ηA, can be redefined as a ratio of the screen relative to

the concentration to the total relative concentration (screen plus filter) for this study, and

can be expressed as:

)1/( WLCCC

AFSM

SMA −+=η (4-5)

To verify the computational results, it is desired to have not only data on

penetration but also on the screen pressure drop. Two pressure taps were installed on the

screen holder, one on the upstream side of the screen, the other on the downstream side.

A digital manometer was used to measure the screen pressure drop to ±0.01 inches of

water. The particular digital manometer has a range of 0 to 10 inches of water. For

pressure drops above 10 inches of water, a conventional U-tube manometer was used.

Experimental Results

For four different types of screens (electroformed-wire, woven-wire, welded-wire,

and perforated-sheet), the experimental measurements of efficiency were made with

particle sizes ranging from 3 to 20 µm AD. Due to the micrometer particle size involved

in the impaction regime, an experimental measurement of pure mechanism (interception,

inertial impaction or gravitation) is very difficult. Most of the deposition phenomenon

includes the combination of mechanisms. Hence, the actual efficiency measured in this

section will be considered the impaction, interception, and gravitational effects. The flow

rate was varied between 80 to 2500 L/min. The results of the screen efficiency

measurements are shown in Figures 4.11 to 4.22. In these figures, ηA is the actual

49

Stokes number, Stk0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1SM/(AF+SM)SM/(AF/(1-WL)+SM)

Figure 4.11. Actual efficiency as a function of Stokes number for electroformed-wire screen (45×45, 0.00138-inch, 0.88).

Stokes number, Stk0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1SM/(AF+SM)SM/(AF/(1-WL)+SM)

Figure 4.12. Actual efficiency as a function of Stokes number for electroformed-wire screen (20×20, 0.00257-inch, 0.90).

50

Stokes number, Stk0.01 0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

SM/(AF+SM)SM/(AF/(1-WL)+SM)

Figure 4.13. Actual efficiency as a function of Stokes number for woven-wire screen (20×20, 0.017-inch, 0.436).

Stokes number, Stk0.01 0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

SM/(AF+SM)SM/(AF/(1-WL)+SM)

Figure 4.14. Actual efficiency as a function of Stokes number for woven-wire screen (64×64, 0.0045-inch, 0.507).

51

Stokes number, Stk0.01 0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

SM/(AF+SM)SM/(AF/(1-WL)+SM)

Figure 4.15. Actual efficiency as a function of Stokes number for woven-wire screen (16×16, 0.018-inch, 0.507).

Stokes number, Stk0.01 0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

SM/(AF+SM)SM/(AF/(1-WL)+SM)

Figure 4.16. Actual efficiency as a function of Stokes number for woven-wire screen (30×30, 0.0095-inch, 0.511).

52

Stokes number, Stk0.01 0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

SM/(AF+SM)SM/(AF/(1-WL)+SM)

Figure 4.17. Actual efficiency as a function of Stokes number for woven-wire screen (16×16, 0.016-inch, 0.554).

Stokes number, Stk0.01 0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

SM/(AF+SM)SM/(AF/(1-WL)+SM)

Figure 4.18. Actual efficiency as a function of Stokes number for woven-wire screen (14×14, 0.017-inch, 0.581).

53

Stokes number, Stk0.01 0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

SM/(AF+SM)SM/(AF/(1-WL)+SM)

Figure 4.19. Actual efficiency as a function of Stokes number for woven-wire screen (16×16, 0.0095-inch, 0.719).

Stokes number, Stk0.01 0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

SM/(AF+SM)SM/(AF/(1-WL)+SM)

Figure 4.20. Actual efficiency as a function of Stokes number for welded-wire screen (8×8, 0.017-inch, 0.746).

54

Stokes number, Stk0.01 0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

SM/(AF+SM)SM/(AF/(1-WL)+SM)

Figure 4.21. Actual efficiency as a function of Stokes number for perforated-sheet screen (0.015-inch, 0.21).

Stokes number, Stk0.01 0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

SM/(AF+SM)SM/(AF/(1-WL)+SM)

Figure 4.22. Actual efficiency as a function of Stokes number for perforated-sheet screen (0.1875-inch, 0.51).

55

efficiency, corrected from the aerosol collection in the screen, and it is compared between

with wall loss and without wall loss, calculated by means of Equations (4-3 and 4-5). The

actual efficiency is plotted as a function of Stokes number for each screen. It is seen that

in all cases, the curves are similar in shape, but the slope of each curve is dependent on

the fraction of open area (fOA). The efficiency increases with increasing Stokes number

which is a function of particle diameter, face velocity and characteristic length (dC). The

increase in efficiency with increasing particle size or face velocity can be explained by

the dominance of the inertial impaction collection mechanism where large particles are

collected more efficiently due to their high inertial parameter (Stokes number). Two of

the most important practical problems in screen filtration studies are to predict the

maximum and minimum efficiencies and the corresponding Stokes numbers. In all cases,

the maximum actual efficiency is almost close to the solidity value of each screen as the

Stokes number is increased. Further discussions of these results will be also made in

Chapter VI.

Discussion of Errors

Tables 4.4 to 4.6 summarize predicted uncertainties that may occur in

experimental tests through the Kline and McClintock method (1953).

Uncertainty Evaluation by Klein/McClintock

Y=Y(X1, X2, X3,…) (4-6)

Here, Y: results (e.g., relative concentration), Xi: measured variables (e.g., raw

fluorometer reading in arbitrary units (mf), volume of total solvent used to soak filters (V),

volumetric air flow rate (Q), test duration (t)).

56

iXδ : variation of Xi (specified or estimated) (4-7)

iwX=

i

i

Xδ : uncertainty of Xi (4-8)

ii

i XXYY δδ

∂∂

= : variation of Y by Xi (4-9)

iYii

i

i

i

i

ii

i

i wwXY

YX

XX

XY

YX

XXY

YYY

=∂∂

=∂∂

=∂∂

=δ

δδ 1 (4-10)

Overall uncertainty of Y by all Xi

.......2

22

2

2

11

12221 +⎥

⎦

⎤⎢⎣

⎡∂∂

+⎥⎦

⎤⎢⎣

⎡∂∂

±=++±= wXY

YX

wXY

YX

www YYY (4-11)

A degree of uncertainty is related with data collected through experimental

investigations such as systematic or bias errors and precision or random errors. In the

experimental study, screen aerosol concentration (CSM) and after-filter aerosol

concentration (CAF) were determined using Equation (4-8). Applying the concept of Kline

and McClintock method gives:

2222

⎥⎦

⎤⎢⎣

⎡∂

∂+⎥

⎦

⎤⎢⎣

⎡∂∂

+⎥⎦

⎤⎢⎣

⎡∂∂

+⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

±=tt

tC

Ct

QQ

QC

CQ

VV

VC

CV

mm

mC

Cm

w SM

SM

SM

SM

SM

SMf

f

f

SM

SM

fCSM

δδδδ

(4-12)

The overall uncertainty of the aerosol concentration can be estimated by incorporating

individual uncertainties in the measurable quantities cf, V, Q, and t. If the relative errors

in these parameters (cf, V, Q, t) for relative concentration are estimated to be ±5%, ±2.5%,

±2.5%, ±0.4%, respectively, the overall uncertainty of the screen aerosol concentration

(CSM) is calculated to be ±6.1% using these values in Equation (4-11). Using the same

57

concept, the overall uncertainties of the after-filter aerosol concentration (CAF) are

estimated to be the same value for the screen aerosol concentration (CSM).

If we rewrite the collection efficiency as,

AFSM

SMA CC

C+

=η (4-13)

The relative error in collection efficiency is calculated to be ±8.6%:

22

⎥⎦

⎤⎢⎣

⎡+⎥

⎦

⎤⎢⎣

⎡±=

AF

AF

SM

SME C

CCC

wδδ (4-14)

The uncertainty in the physical particle diameter (dp) which is given by the ratio of the

particle diameter measured (dm) under the microscope to the flattering factor (f) of the

droplet which is a mixture of oleic acid and sodium fluorescien is given by:

22

⎥⎦

⎤⎢⎣

⎡+⎥

⎦

⎤⎢⎣

⎡±=

ff

dd

wm

mdP

δδ (4-15)

It is estimated that δdm/dm has ±2.9%, ±1.7%, ±1.2% and ±1.1% for 1-5 µm, 6-10 µm, 11-

15 µm and <16 µm particle sizes, respectively, and δf/f has ±3% as determined by an

approach similar to that by Olan-Figueroa et al. (1982). The overall uncertainty in

particle size determination, given by Equation (4-11), is ±4.2%, ±3.4%, ±3.2% and

±3.2% for 1-5 µm, 6-10 µm, 11-15 µm and <16 µm AD particle sizes, respectively.

Additional important parameters that require the estimation of uncertainty is the Stokes

number. If we rewrite the Stokes number as,

c

o2

ppp

c

o2

ppc

dµ18

Udρ)d

λ2.34(1

dµ18UdρC

Stk⋅⋅

⋅⋅⋅⋅

+

=⋅⋅

⋅⋅⋅= (4-16)

58

The relative error in calculating the Stokes number for a given particle size may be

expressed as:

222

34.234.22

⎥⎦

⎤⎢⎣

⎡+⎥

⎦

⎤⎢⎣

⎡+

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅+

⋅+⋅±=

c

c

o

o

p

p

p

pStk d

dUU

dd

dd

wδδδ

λλ

(4-17)

The relative errors in the particle size dp are given by the above calculation for each

particle size, while the errors associated in measuring the velocity Uo is estimated to be

±2.5%. The total uncertainty in the calculated value of the Stokes number is presented in

Tables 4.4 to 4.6 based on the error related in measuring the characteristic length (wire

diameter and effective slack length) for each screen (electroformed-wire, woven-wire,

and perforated-sheet).

Table 4.4. The total predicted uncertainty in the calculated value of Stokes number for electroformed-wire.

Particle Size δdp/dp δUo/Uo δdc/dc wstk

(AD µm)

1 to 5 µm 4.2% 2.5% 3.0% 7.7% 6 to10 µm 3.4% 2.5% 3.0% 7.4% 11 to15 µm 3.2% 2.5% 3.0% 7.2%

< 16 µm 3.2% 2.5% 3.0% 7.3%

59

Table 4.5. The total predicted uncertainty in the calculated value of Stokes number for woven-wire.

Particle Size δdp/dp δUo/Uo δdc/dc wstk δdc/dc wstk δdc/dc wstk

(AD µm)

dw < 0.005-inch 0.005 ≤ dw ≤ 0.01 dw > 0.01

1 to 5 µm 4.2% 3% 2.1% 7.4% 3.5% 7.9% 2.5% 7.5%6 to10 µm 3.4%

3% 2.1% 7.0% 3.5% 7.6% 2.5% 7.2%11 to15µm 3.2% 3% 2.1% 6.9% 3.5% 7.4% 2.5% 7.0%< 16 µm 3.2% 3% 2.1% 6.9% 3.5% 7.5% 2.5% 7.1%

Table 4.6. The total predicted uncertainty in the calculated value of Stokes number for perforated-sheet. Particle

Size δdp/dp δUo/Uo δdc/dc wstk

(AD µm)

1 to 5 µm 4.2% 2.5% 3.0% 7.7%6 to10 µm

3.4% 2.5% 3.0% 7.4%11 to15 µm 3.2% 2.5% 3.0% 7.2%

< 16 µm 3.2% 2.5% 3.0% 7.3%

60

CHAPTER V

NUMERICAL STUDIES

Three-dimensional numerical simulations corresponding to the various

experimental investigations were conducted using commercial computational fluid

dynamics (CFD) software, Fluent (version 6.1.22), as a tool. The deposition process was

modeled as a dilute and disperse two-phase flow problem under the Eulerian-Lagrangian

framework, with an assumed one-way coupling between the phases. This implies that a

convergent flow field is first obtained for the domain of interest and aerosol particles are

released at appropriate locations and their trajectories computed as a post-processing

operation, to determine deposition on the screen. The predicted numerical results were

then compared with the experimental results.

Different configurations were investigated in scoping simulations with the

appropriate boundary conditions to determine the right combination of configuration and

boundary conditions (computational model), that is a proper numerical representation of

the aerosol particle deposition process on a screen. Figure 5.1 shows the different models

that were investigated. The computational model deduced from the results of the scoping

simulations was used as the base model for subsequent investigations.

A block-structured body-fitted coordinate system was used for discretization of

the simulation domain to suit the nature of the domain and a structured, hexahedral grid

was generated on the domain. The total number of nodes was different depending on each

screen configuration in this study. Gambit (the topology-generating a grid-

61

(a) Wire screen

(b) Perforated-sheet screen

Figure 5.1. Schematic for the idealization of numerical analysis on the screen.

62

generating module of Fluent) was used to create the mesh which consisted of 1.8 to 2.2

million computational nodes. Effect of different solution algorithms for the pressure-

velocity coupling such as SIMPLE, SIMPLEC (SIMPLE-Consistent), PISO, and different

discretization schemes for the convective terms on the resolution of the flow-field and the

consequent impact on the particle deposition process were analyzed. The acronym

SIMPLE stands for Semi-Implicit Method for Pressure-Linked Equations (Patankar

1980). The condition of convergence, called residuals, was selected as of the

overall conservation of the flow properties.

5101 −×

Flow Field Simulation

The flow field is setup through the use of Fluent. The continuity equation used for

steady state, incompressible, Newtonian flow is:

0)(=

∂∂

i

i

xu (5-1)

Here, ui is the flow velocity in the ith direction.

The momentum equation is given as:

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂

∂+

∂∂

∂∂

+∂∂

−=∂

∂)(

)(

i

j

j

i

ii

s

i

ji

xu

xu

xxP

xuu

µρ

(5-2)

where is the static pressure. sP

In viscous flows, the no-slip boundary condition is imposed by default on all wall

surfaces in the computational grid. A uniform velocity profile is specified at the inlet,

based on the experimental conditions. As shown in Figure 5.2, a channel is isolated for

63

(a) Wire screen

(b) Perforated-sheet screen

Figure 5.2. Schematic of the numerical setup used to study the screen deposition process.

64

analysis purposes by employing periodic boundary conditions at the interfaces with the

neighbor channels. Outflow boundary conditions in Fluent are imposed to model flow

exits, where the details of the flow velocity and pressure are not known prior to solution

of the flow problem. With this boundary condition, no other conditions are needed at the

outflow boundaries: Fluent extrapolates the required information from the interior of the

flow field.

Particle Tracking Methodology

In addition to solving transport equations for the continuous phase, Fluent allows

simulation of a discrete second phase in a Lagrangian frame of reference. This second

phase consists of spherical aerosol particles. Coupling between the phases and its impact

on both the discrete phase trajectories and the continuous phase flow can be included.

The trajectory of a particle is predicted through the use of Newton’s equation with

time integration of the forces acting on the particle, and is written in a Lagrangian

reference frame, i.e.:

p

pivuD

v guuF

dtdu

ρρρ )(

)(−

+−= (5-3)

Here, uv is the particle velocity, and FD is the drag force on the particle and is given by

vuvuPDD uuuudCF −−= )()4

(21 2 ρπρ (5-4)

Rep is the particle Reynolds number and is expressed as:

65

µ

ρ uvpp

uud −=Re

)( pD RefC =

Results of scoping simulations performed to determine the appropriate base

configuration, along with details of the different model configurations investigated are

presented in Figure 5.3, for the reference screen material of two different wire diameters

and fraction of open area (a. 20×20 mesh size, dw = 65 µm, fOA = 0.90, b. 64×64 mesh size,

dw = 114 µm, fOA = 0.51) at a wire Reynolds number of 1.0, and compared against

experimental data. The total number of nodes was 1.5 million to 2.1 million depending on

the model configuration. It is evident from Figure 5.3 that predictions obtained for

Model-II-B are in very good agreement to experimental data, compared to the other

models. Hence, Model-II-B was chosen as the base configuration for the present study.

Once the particle velocity components are calculated using the above equations, particle

trajectories can be obtained by solving:

Numerical Results

Physical conditions pertaining to numerical simulations performed in this study

are presented in Table 5.1, which summarizes the tested particle sizes, flow rates (Q),

flow Reynolds number (Re), characteristic length Reynolds number (ReC), interception

parameter (R) and Stokes number (Stk) ranges.

The particle drag coefficient, CD is a function of the particle Reynolds number.

vv u

dtdx

= (5-7)

(5-6)

(5-5)

Table 5.1. Operation condition of numerical simulations for each screen.

Screen Fraction of Mesh Particle size Q Re Re C R StkType Open Area Size

(f OA ) (M) AD Min-Max Min-Max Min-Max Min-Max Min-Maxinch µm % µm L/min

1 Electroformed 0.00629 160 56.0 40 4-20 164-1644 1542-15424 3-30 0.025-0.125 0.51-12.292 Electroformed 0.00268 68 75.0 50 4-20 86-861 808-8080 0.5-5 0.059-0.294 0.49-15.113 Electroformed 0.00138 35 88.0 45 3-20 78-1960 732-18392 0.5-5 0.057-0.571 0.54-20.344 Electroformed 0.00257 65 90.0 20 4-20 44-1080 408-10135 0.5-5 0.061-0.307 0.58-19.80

3-20 44-1960 408-18392 0.5-30 0.025-0.571 0.49-20.34

1 Woven 0.01700 432 43.6 20 3-20 47-2368 444-22217 3-150 0.007-0.046 0.12-6.552 Woven 0.00450 114 50.7 64 4-20 69-693 651-6507 1-10 0.035-0.175 0.23-7.253 Woven 0.01800 457 50.7 16 2-20 52-2600 488-24399 3-150 0.007-0.044 0.08-6.794 Woven 0.00950 241 51.1 30 3-20 33-1655 311-15532 1-50 0.012-0.083 0.11-8.195 Woven 0.01600 406 55.4 16 3-20 64-3196 600-29994 3-150 0.007-0.049 0.13-9.396 Woven 0.01700 432 58.1 14 3-20 63-3155 592-29605 3-150 0.007-0.046 0.11-8.737 Woven 0.00950 241 71.9 16 3-20 140-2329 1311-21854 3-50 0.017-0.083 0.34-9.35

2-20 33-3196 311-29994 1-150 0.007-0.175 0.08-9.39

1 Welded 0.01700 432 74.6 8 3-20 270-2700 2534-25342 10-100 0.007-0.046 0.15-7.47

1 Perforated 0.01500 381 21.0 N/A 3-20 81-2423 758-22739 10-341 0.007-0.047 0.16-6.802 Perforated 0.18750 4763 51.0 N/A 6-20 502-2510 4712-23562 115-575 0.003-0.011 0.15-1.64

3-20 81-2510 758-23562 10-575 0.003-0.047 0.15-6.80

Wire diameterHole diameter

(dw or d h )

*Note: Grey highlight is for the overall ranges for each screen.

66

67

Model-I-B Model-II-A Model-II-B Model-III-B Model-I-A Model-I-B Model-II-B Model-III-B

Stokes number, Stk0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

EXPModel-I-BModel-II-AModel-II-BModel-III-B

Stokes number, Stk0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A0.001

0.01

0.1

1

EXPModel-I-AModel-I-BModel-II-BModel-III-B

(a) 20×20 mesh size, dw = 65 µm, fOA = 0.90 (b) 64×64 mesh size, dw = 114 µm, fOA = 0.51

Figure 5.3. Result of the numerical model iteration.

68

Additionally in Figure 5.4, the comparison of collection efficiency between the ideal

model (with symmetric BC’s) and the actual model (with symmetric BC’s) was carried

out with one of the woven-wires (14×14-mesh size, dw = 0.017-inch, fOA = 0.581).

For 14 screens (4 electroformed-wire, 7 woven-wire, 1 welded-wire screen and 2

perforated-sheet screens), the actual efficiency calculations were made with particle sizes

ranging from 2 to 20 µm and Stokes number ranging from 0.08 to 20.34. The actual

efficiency is plotted as a function of particle size for different Reynolds numbers (ReC)

and as a function of Stokes number, as shown in Figures 5.5 through 5.18.

It is seen that in all cases the curves are similar in shape and the log-log plot of

actual efficiency against particle size leads to a curve whose slope and critical particle

size both depend on characteristic length Reynolds number. The minimum particle size

decreases with increasing Reynolds number, showing the increasingly important role of

the inertial impaction mechanisms. There are certain very interesting features to be

observed from the presented results. The obtained results show that the same Stk values

lead to the same collection behavior on the screen. This emphasizes that characteristic

length Reynolds number is not a unique parameter to describe the collection behavior in

that regime. These results will be discussed further when comparison with the

experimental results is made.

69

Stokes number, Stk0.01 0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

EXPNUM: Ideal model w/ symmetric B.C.NUM: Real model w/ symmetric B.C.

(a) Ideal model (b) Real model Figure 5.4. Comparison of efficiency as a function of Stokes number between the ideal model (with symmetric boundary condition) and the real model (with symmetric boundary condition) of numerical simulation with one of woven-wire screen (14×14 mesh, dw = 0.017-inch, fOA = 0.581).

70

Particle size, AD µm

1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

ReC=3.0ReC=5.0ReC=10.0ReC=30.0

(a) ηA vs. Particle size (AD µm)

Stokes number, Stk0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

(b) ηA vs. Stk

Figure 5.5. Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for electroformed-wire screen (40×40, 0.00629-inch, 0.56).

71

Particle size, AD µm

1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

ReC=0.5ReC=1.0ReC=3.0ReC=5.0

(a) ηA vs. Particle size (AD µm)

Stokes number, Stk0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

(b) ηA vs. Stk

Figure 5.6. Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for electroformed-wire screen (50×50, 0.00268-inch, 0.75).

72

Particle size, AD µm

1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

ReC=0.2ReC=0.5ReC=1.0ReC=5.0

(a) ηA vs. Particle size (AD µm)

Stokes number, Stk0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

(b) ηA vs. Stk

Figure 5.7. Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for electroformed-wire screen (45×45, 0.00138-inch, 0.88).

73

Particle size, AD µm

1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1ReC=0.2ReC=0.5ReC=1.0ReC=5.0

(a) ηA vs. Particle size (AD µm)

Stokes number, Stk0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

(b) ηA vs. Stk

Figure 5.8. Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for electroformed-wire screen (20×20, 0.00257-inch, 0.90).

74

Particle size, AD µm

1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

ReC=3.0ReC=5.0ReC=10.0ReC=50.0ReC=100.0ReC=150.0

(a) ηA vs. Particle size (AD µm)

Stokes number, Stk0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

(b) ηA vs. Stk

Figure 5.9. Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for woven-wire screen (20×20, 0.017-inch, 0.436).

75

Particle size, AD µm

1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

ReC=1.0ReC=3.0ReC=5.0ReC=10.0

(a) ηA vs. Particle size (AD µm)

Stokes number, Stk0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

(b) ηA vs. Stk

Figure 5.10. Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for woven-wire screen (64×64, 0.0045-inch, 0.507).

76

Particle size, AD µm

1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

ReC=3.0ReC=5.0ReC=10.0ReC=50.0ReC=100.0ReC=150.0

(a) ηA vs. Particle size (AD µm)

Stokes number, Stk0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

(b) ηA vs. Stk

Figure 5.11. Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for woven-wire screen (16×16, 0.018-inch, 0.507).

77

Particle size, AD µm

1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

ReC=1.0ReC=3.0ReC=5.0ReC=10.0ReC=50.0

(a) ηA vs. Particle size (AD µm)

Stokes number, Stk0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

(b) ηA vs. Stk

Figure 5.12. Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for woven-wire screen (30×30, 0.0095-inch, 0.511).

78

Particle size, AD µm

1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

ReC=3.0ReC=5.0ReC=10.0ReC=50.0ReC=100.0ReC=150.0

(a) ηA vs. Particle size (AD µm)

Stokes number, Stk0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

(b) ηA vs. Stk

Figure 5.13. Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for woven-wire screen (16×16, 0.016-inch, 0.554).

79

Particle size, AD µm

1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

ReC=3.0ReC=5.0ReC=10.0ReC=50.0ReC=100.0ReC=150.0

(a) ηA vs. Particle size (AD µm)

Stokes number, Stk0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

(b) ηA vs. Stk

Figure 5.14. Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for woven-wire screen (14×14, 0.017-inch, 0.581).

80

Particle size, AD µm

1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

ReC=3.0ReC=5.0ReC=10.0ReC=50.0

(a) ηA vs. Particle size (AD µm)

Stokes number, Stk0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

(b) ηA vs. Stk

Figure 5.15. Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for woven-wire screen (16×16, 0.0095-inch, 0.719).

81

Particle size, AD µm

1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

ReC=10.0ReC=50.0ReC=100.0

(a) ηA vs. Particle size (AD µm)

Stokes number, Stk0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1

(b) ηA vs. Stk

Figure 5.16. Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for welded-wire screen (8×8, 0.017-inch, 0.746).

82

Particle size, AD µm

1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

ReC=10.5

ReC=52.3ReC=104.7ReC=314.1

(a) ηA vs. Particle size (AD µm)

Stokes number, Stk0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1

(b) ηA vs. Stk

Figure 5.17. Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for perforated-sheet screen (0.017-inch, 0.21).

83

Particle size, AD µm

1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

ReC=115.0ReC=345.0ReC=575.0

(a) ηA vs. Particle size (AD µm)

Stokes number, Stk0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1

(b) ηA vs. Stk

Figure 5.18. Actual efficiency as a function of (a) particle size (AD µm), (b) Stokes number (Stk) for perforated-sheet screen (0.072-inch, 0.51).

84

CHAPTER VI

COMPARISON OF EXPERIMENTAL AND NUMERICAL STUDIES

It was seen in the previous chapter that in the process of short-listing the

computational model to be used in the current research, we used experimental data as the

basis for determination. The purpose of this chapter is to carry forward from that

approach and compare the experimental and numerical results presented in the previous

chapters (IV and V). The first comparisons are made on the basis of the actual efficiency

and then the data collected during the experimental and numerical portions of this study

are used to develop mathematical models. Multiple-regression analysis and curve fitting

was used to develop the models by fitting experimental and numerical data and

determining correlation coefficients. The first empirical models expressed the actual

efficiency in terms of the solidity (αΑ) and Stokes number (Stk). A theoretical

methodology is subsequently developed based on the above data to standardize collection

characteristics of each screen type, whereby, aerosol deposition is expressed as a function

of non-dimensional parameters such as the interception parameter (R), Reynolds number

(ReC), and Stokes number (Stk), that govern the deposition. Further, experimental

measurements and numerical predictions of pressure drop across the screen are used to

develop models for the pressure coefficient in terms of the fraction of open area (fOA) and

Reynolds number.

85

Comparison with Actual Efficiencies

Both numerical and experimental studies have been conducted on electroformed-

wire, woven-wire, welded-wire screens and perforated-sheet screens. Results for all the

cases, presented as a log-log plot of the actual efficiency (ηA) against Stk, leads to a curve

whose slope depend on the solidity (αA). The plots are provided with bi-directional error

bars for experimental measurements, where, vertical error bars represent the standard

deviation in the estimated collection efficiency values, while the horizontal error bars

represent the uncertainty involved in the calculation of Stokes number values (based on

the discussion of errors in Chapter IV).

Figure 6.1 presents a direct comparison of the numerical predictions with

experimental results for the 20×20 and 45×45 mesh screens, over a wide range of wire

Reynolds numbers (0.5 to 30). It can be seen that the agreement is very good, indicating

that the computations are able to reproduce the actual trend. The above results validate

the accuracy of the numerical approach and indicate that the procedure can be used with

confidence in the future research. Having validated the numerical procedure, simulations

were performed to obtain predictions of collection characteristics of 40×40 and 50×50

mesh screens and the results are also presented in Figure 6.1.

Figure 6.2 shows comparisons of the actual efficiency from experimental

measurements and numerical predictions for eight woven-wire screens with mesh sizes

ranging from 14×14 to 64×64 and fraction of open area from 0.436 to 0.719 in the wire

Reynolds number range of 1 to 158. Figure 6.3 shows comparisons of the individual

actual efficiencies versus Stokes number. It can be seen that there is a fairly good

agreement between experimental and numerical results, even though the ideal model was

Figure 6.4 shows a comparison of the actual efficiencies for the experimental and

numerical cases for the welded screen with a mesh size of 8×8 and fraction of open area

at 0.746 for wire Reynolds numbers from 10 to 100.

used in the numerical study instead of the real woven-wire model. The slight discrepancy

noticed for some of the case may be explained by the non-ideal nature of the woven-wire

screen, as in a real screen, the wires are not distributed uniformly and not all are

perpendicular to the flow direction.

Figure 6.1. Comparison of actual efficiency predictions for electroformed-wires to experimental and numerical data (ReC = 0.5 to 30). Parameters in legend are mesh size, wire diameter (µm) and fraction of open area (fOA).

Stokes number, Stk0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

EXP.: 45X45, 35, 0.88EXP.: 20X20, 65, 0.90NUM.: 40X40, 160, 0.56NUM.: 50X50, 68, 0.75NUM.: 45X45, 35, 0.88NUM.: 20X20, 65, 0.90

86

Stokes number, Stk0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1EXP.: 20x20, 432, 0.436EXP.: 64x64, 114, 0.507EXP.: 16x16, 457, 0.507EXP.: 30x30, 241, 0.511EXP.: 16x16, 406, 0.554EXP.: 14x14, 432, 0.581EXP.: 16x16, 241, 0.719NUM.: 20x20, 432, 0.436NUM.: 64x64, 114, 0.507NUM.: 16x16, 457, 0.507NUM.: 30x30, 241, 0.511NUM.: 16x16, 406, 0.554

NUM.: 14x14, 432, 0.581NUM.: 16x16, 241, 0.719

Figure 6.2. Comparison of actual efficiency predictions for woven-wires to experimental and numerical data (ReC = 1 to 158).

Parameters in label are mesh size, wire diameter (µm) and fraction of open area.

87

88

Stokes number, Stk0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1EXPERIMENTALNUMERICAL

Stokes number, Stk

0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1EXPERIMENTALNUMERICAL

Stokes number, Stk

0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1EXPERIMENTALNUMERICAL

Stokes number, Stk

0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1EXPERIMENTALNUMERICAL

(a) 20×20, 0.017, 0.436 (b) 64×64, 0.0045, 0.507 (c) 16×16, 0.018, 0.507 (d) 30×30, 0.0095, 0.511

Stokes number, Stk0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1EXPERIMENTALNUMERICAL

Stokes number, Stk

0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

Α

0.01

0.1

1EXPERIMENTALNUMERICAL

Stokes number, Stk

0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1EXPERIMENTALNUMERICAL

(e) 16×16, 0.016, 0.554 (f) 14×14, 0.017, 0.581 (g) 16×16, 0.0095, 0.719 Figure 6.3. Comparison of actual efficiency predictions for woven-wires to experimental data (ReC = 1 to 158). Parameters in label are mesh size, wire diameter (µm) and fraction of open area.

89

Stokes number, Stk0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1

EXP.: 8x8, 432, 0.746NUM.: 8x8, 432, 0.746

Figure 6.4. Comparison of actual efficiency predictions for welded-wires to experimental and numerical data (ReC = 10 to 100). Parameters in label are mesh size, wire diameter (µm) and fraction of open area.

Figure 6.5 shows a comparison of actual efficiency from experimental and

numerical studies for perforated-sheets with two different fractions of open area (0.21

and 0.51) in the effective slack Reynolds number ranging from 10 to 575.

Numerical predictions are seen to be in very good agreement to the experimental

data. There are certain very interesting features to be observed from the presented results.

First, it can be seen that the log-log plot of ηA against Stk leads to a curve whose slope

depend on the areal solidity (αA). An increase in the collection efficiency through a

reduction of the opening size to a neighboring wire may be explained by the compression

90

Stokes number, Stk0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1

EXP.: 425, 0.21EXP.: 1826, 0.51NUM.: 425, 0.21NUM.: 1826, 0.51

Figure 6.5. Comparison of actual efficiency predictions for perforated-sheet to experimental and numerical data (ReC =10 to 575). Parameters in label are effective slack length (µm) and fraction of open area. of the fluid streamlines in the vicinity of the wires as a result of continuity. Second,

results show that beginning at critical Stokes number (Stkc), efficiency increased

gradually to its maximum value that was almost asymptotic to its solidity for that

particular screen, at higher Stokes numbers.

Actual Efficiency Modeling

Literature presents relatively few studies that have developed mathematical

models for screens to describe collection efficiency. Most of the earlier studies were

performed with fibrous filter under conditions where diffusion, interception and inertial

Where C1, C2, and C3 are functions of the solidity (αA). The values of C1, C2, and

C3 are obtained by a regression analysis of the combined experimental and numerical

data and are listed in Table 6.1 for each screen. Further regression analyses for C1, C2,

and C3 were performed as a function of the solidity (αA). These are shown in Figures 6.6

and 6.8 respectively. The functions C1, C2, and C3 turned out to be a function of the

solidity, at least in the range of αA tested in this study (0.10 ≤ αA ≤ 0.79). Therefore,

Equation (6-1) is modified to the following.

impaction effects were considered. The present study examined flow at low and

intermediate characteristic length Reynolds number conditions to obtain a better

understanding of the factors that influence variation in screen efficiency.

In all the cases, the log-log plot of actual efficiency (ηA) against Stokes number

leads to a curve whose slope and y-intercept both depend on the solidity (αA) as shown in

Figures 6.1 through 6.5. The relationship between the actual efficiency and Stokes

number can be obtained in initial form (Hyperbolic, 3 parameters) using a commercial

graphing software (SigmaPlot 2004).

With further regression, the constants, z0, z1, z2, z3, z4, and z5 for all screens were

calculated and are listed in Table 6.2 due to express a final correlation between the actual

efficiency and the solidity and Stokes number. Therefore, the final correlation for each

screen can be expressed as

3

21

1CStk

CCA

++=η

)(1

)()(

54

3210

A

AAA

zzStkzzzz

α

ααη

++

+++=

(6-1)

(6-2)

91

Table 6.1 Values of C1, C2, and C3 in Equation (6-1) obtained by regression analysis.

Screen Fraction of Mesh Solidity R2

Type Open Area Size(f OA) (αA) Value StdErr Value StdErr Value StdErr

inch µm

Electroformed 0.00629 160 0.56 40 0.44 0.4370 0.0008 -0.7260 0.0052 0.6677 0.0107 0.9997Electroformed 0.00268 68 0.75 50 0.25 0.2578 0.0005 -0.3561 0.0012 1.1680 0.0134 0.9998Electroformed 0.00138 35 0.88 45 0.12 0.1213 0.0010 -0.1880 0.0028 0.8679 0.0431 0.9969Electroformed 0.00257 65 0.90 20 0.10 0.1038 0.0006 -0.1450 0.0024 1.1660 0.0552 0.9962

Woven 0.0170 432 0.44 20 0.56 0.5601 0.0069 -0.6322 0.0075 0.5857 0.0360 0.9908Woven 0.0045 114 0.51 64 0.49 0.4958 0.0065 -0.6700 0.0160 0.5474 0.0432 0.9892Woven 0.0180 457 0.51 16 0.49 0.4819 0.0078 -0.5201 0.0073 0.6222 0.0454 0.9826Woven 0.0095 241 0.51 30 0.49 0.4893 0.0048 -0.5263 0.0048 0.7654 0.0329 0.9944Woven 0.0160 406 0.55 16 0.45 0.4623 0.0049 -0.5226 0.0051 0.7719 0.0396 0.9928Woven 0.0170 432 0.58 14 0.42 0.4340 0.0023 -0.4785 0.0043 0.7458 0.0140 0.9980Woven 0.0095 241 0.72 16 0.28 0.3083 0.0103 -0.3422 0.0083 1.0520 0.1180 0.9828

Welded 0.0170 432 0.75 8 0.25 0.2685 0.0073 -0.2955 0.0076 0.9604 0.1256 0.9733

Perforated 0.0150 381 0.21 N/A 0.79 0.7445 0.0081 -1.3220 0.0886 0.1669 2.10E-02 0.9830Perforated 0.1875 4763 0.51 N/A 0.49 0.4425 0.0147 -0.7329 0.0610 0.1859 4.05E-02 0.9755

(dw or d h)

C1 C2 C 3Wire diameterHole diameter

92

Solidity, αA

0.0 0.2 0.4 0.6 0.8 1.0

C1

0.0

0.5

1.0

1.5

2.0

Solidity, αA

0.0 0.2 0.4 0.6 0.8 1.0

C2

-2.0

-1.5

-1.0

-0.5

0.0

Solidity, αA

0.0 0.2 0.4 0.6 0.8 1.0

C3

0.0

0.5

1.0

1.5

2.0

(a) C1 vs. αA (b) C2 vs. αA (c) C3 vs. αA

Figure 6.6. The functions C1, C2, and C3 of Equation (6-1) for electroformed-wire screens.

Solidity, αA

0.0 0.2 0.4 0.6 0.8 1.0

C1

0.0

0.5

1.0

1.5

2.0

Solidity, αA

0.0 0.2 0.4 0.6 0.8 1.0

C2

-1.0-0.8-0.6-0.4-0.20.0

Solidity, αA

0.0 0.2 0.4 0.6 0.8 1.0

C3

0.0

0.5

1.0

1.5

2.0

(a) C1 vs. αA (b) C2 vs. αA (c) C3 vs. αA

Figure 6.7. The functions C1, C2, and C3 of Equation (6-1) for woven-wire and welded-wire screens.

93

94

Solidity, αA

0.0 0.2 0.4 0.6 0.8 1.0

C1

0.0

0.5

1.0

1.5

2.0

Solidity, αA

0.0 0.2 0.4 0.6 0.8 1.0

C2

-2.0

-1.5

-1.0

-0.5

0.0

Solidity, αA

0.0 0.2 0.4 0.6 0.8 1.0

C3

0.0

0.5

1.0

1.5

2.0

(a) C1 vs. αA (b) C2 vs. αA (c) C3 vs. αA

Figure 6.8. The functions C1, C2, and C3 of Equation (6-1) for perforated-sheet screens.

Table 6.2 Values of z0, z1, z2, z3, z4, and z5 in Equation (6-2) obtained by regression analysis. Screen

Type R 2 R 2 R 2

Value StdErr Value StdErr Value StdErr Value StdErr Value StdErr Value StdErr

Electroformed 0.006 0.005 0.985 0.018 0.999 0.029 0.029 -1.682 0.109 0.998 1.149 0.210 -1.018 0.661 0.542

Woven 0.066 0.016 0.870 0.034 0.993 -0.053 0.071 -1.029 0.165 0.886 1.516 0.163 -1.735 0.352 0.829

Perforated -0.051 0.000 1.007 0.000 1.000 0.213 0.000 -1.943 0.000 1.000 0.217 0.000 -0.063 0.000 1.000

C 1 =z o +z 1α A C 2 =z 2 +z 3α A C 3 =z 4 +z 5α A

z 0 z 1 z 2 z 3 z 4 z 5

95

electroformed-wires:

)018.1149.1(1

)682.102889.0()9852.0005838.0(

A

AAA Stk

α

ααη

−+

−++=

0.10≤ αA ≤0.44, 0.49≤ Stk ≤20 (6-3)

woven-wires:

)735.1516.1(1

)029.105282.0()8704.006565.0(

A

AAA Stk

α

ααη

−+

−−++=

0.28≤ αA ≤0.56, 0.11≤ Stk ≤9.39 (6-4)

welded-wire:

9604.01

)2955.0(2685.0 StkA

+

−+=η

αA = 0.25, 0.16≤ Stk ≤7.47 (6-5)

perforated-sheets:

)0633.02169.0(1

)943.12132.0()007.105077.0(

A

AAA Stk

α

ααη

−+

−++−=

0.49≤ αA ≤0.79, 0.13≤ Stk ≤6.93 (6-6)

Figures 6.9 to 6.12 present correlation plots between the measured and calculated

efficiencies that provide a confidence estimate on these correlations. Actual efficiency

values obtained from experimental and numerical results are plotted as function of the

correlated actual efficiency based on these correlations with error bar which are

calculated with the uncertainty (wηA, measured).

96

Measured actual efficiency, ηΑ,Measured

0.01 0.1 1

Cor

rela

ted

actu

al e

ffic

ienc

y (E

q. 6

-3), η Α

,Cor

r.

0.01

0.1

1

Reference line (1:1 Ratio)

Measured actual efficiency, ηΑ,Measured

0.01 0.1 1

Cor

rela

ted

actu

al e

ffic

ienc

y (E

q. 6

-3), η Α

,Cor

r.

0.01

0.1

1Reference line (1:1 Ratio)

SSE = 0.003 < 0.086 = wηA,Measured SSE = 0.006 < 0.086 = wηA,Measured

Figure 6.9. Comparison between the experimentally and numerically measured actual efficiency and correlated actual efficiency based on correlation (Equation 6-3) for electroformed-wire screens.

(a) 40×40, 160, 0.56 (b) 50×50, 68, 0.75

Measured actual efficiency, ηΑ,Measured

0.01 0.1 1

Cor

rela

ted

actu

al e

ffic

ienc

y (E

q. 6

-3), η Α

,Cor

r.

0.01

0.1

1Reference line (1:1 Ratio)

Measured actual efficiency, ηΑ,Measured

0.01 0.1 1

Cor

rela

ted

actu

al e

ffic

ienc

y (E

q. 6

-3), η Α

,Cor

r.

0.01

0.1

1Reference line (1:1 Ratio)

SSE = 0.0004 < 0.086 = wηA,Measured SSE = 0.002 < 0.086 = wηA,Measured (c) 45×45, 35, 0.88 (d) 20×20, 65, 0.90

97

ηΑ,Measured

0.01 0.1 1

η Α,C

orr.,

(Eq.

6-4

)

0.01

0.1

1Reference line (1:1 Ratio)

ηΑ,Measured

0.01 0.1 1

η Α,C

orr.,

(Eq.

6-4

)

0.01

0.1

1

Reference line (1:1 Ratio)

ηΑ,Measured

0.01 0.1 1

η Α,C

orr.,

(Eq.

6-4

)

0.01

0.1

1Reference line (1:1 Ratio)

ηΑ,Measured

0.01 0.1 1

η Α,C

orr.,

(Eq.

6-4

)

0.01

0.1

1Reference line (1:1 Ratio)

SSE = 0.031 SSE = 0.073 SSE = 0.047 SSE = 0.022 (a) 20×20, 432, 0.436 (b) 64×64, 114, 0.507 (c) 16×16, 457, 0.507 (d) 30×30, 241, 0.511

Figure 6.10. Comparison between the experimentally and numerically measured actual efficiency and correlated actual efficiency based on correlation (Equation 6-4) for woven-wire screens.

ηΑ,Measured

0.01 0.1 1

η Α,C

orr.,

(Eq.

6-4

)

0.01

0.1

1Reference line (1:1 Ratio)

ηΑ,Measured

0.01 0.1 1

η Α,C

orr.,

(Eq.

6-4

)

0.01

0.1

1Reference line (1:1 Ratio)

ηΑ,Measured

0.01 0.1 1

η Α,C

orr.,

(Eq.

6-4

)

0.01

0.1

1Reference line (1:1 Ratio)

SSE = 0.021 SSE = 0.011 SSE = 0.024 (e) 16×16, 406, 0.554 (f) 14×14, 432, 0.581 (g) 16×16, 241, 0.719

98

Measured actual efficiency, ηΑ,Measured

0.01 0.1 1

Cor

rela

ted

actu

al e

ffic

ienc

y (E

q. 6

-5), η Α

,Cor

r.

0.01

0.1

1Reference line (1:1 Ratio)

SSE = 0.006

Figure 6.11. Comparison between the experimentally and numerically measured actual efficiency and correlated actual efficiency based on correlation (Equation 6-5) for welded-wire screen.

Measured actual efficiency, ηΑ,Measured

0.01 0.1 1

Cor

rela

ted

actu

al e

ffic

ienc

y (E

q. 6

-6), η Α

,Cor

r.

0.01

0.1

1

Reference line (1:1 Ratio)

Measured actual efficiency, ηΑ,Measured

0.01 0.1 1

Cor

rela

ted

actu

al e

ffic

ienc

y (E

q. 6

-6), η Α

,Cor

r.

0.01

0.1

1

Reference line (1:1 Ratio)

SSE = 0.039 SSE = 0.010

(a) 425, 0.21 (b) 1826, 0.51 Figure 6.12. Comparison between the experimentally and numerically measured actual efficiency and correlated actual efficiency based on correlation (Equation 6-6) for perforated-sheet screens.

99

The solid line is a reference line which has a ratio of one between the two

efficiencies. There are certain very interesting features to be observed from the presented

results. First, it can be seen visually whether the calculated actual efficiency under-

predicts or over-predicts based on the reference line. Second, a residue is the difference

between the measured and correlated value of a function. Some residues are positive and

others negative. If we add up the squares of the residues, we get a measure of how well

the line fits, called the Sum-of-Squares error (SSE). The SSE of the measured data is

approximated by a function that is given by

SSE = Sum of squares of residues (6-7)

= Sum of (ymeasured – ycorrelated)2

The smaller SSE, the better the approximating function fits the data. Additionally, in all

the cases (Figures 6.9 to 6.12) the SSE should be less than the uncertainty of measured

value. If the SSE is larger than the experimental uncertainty value, the correlation

equation is not valid for predicting values. There is another statistical approach to report

this result whether mathematical models (Equations 6-3 to 6-6) are best-fit for measured

results. The p value from a paired t-test in statistic was less than 0.01 for these models

(Equations 6-3 to 6-6) in the case of 99% confidence intervals. Figures 6.13 to 6.16 were

re-plotted to compare with the experimentally and numerically measured efficiency and

the calculated efficiency, in addition to gray curves that were based on correlation

Equations (6-3 to 6-6). They can be seen that the gray curves indicate exactly similar

collection trends compared to measured data, are spaced proportionally apart from their

neighbors, and asymptotically approach a maximum efficiency value that is equal to their

areal solidity.

Stokes number, Stk0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

EXP.: 45X45, 35, 0.88EXP.: 20X20, 65, 0.90NUM.: 40X40, 160, 0.56NUM.: 50X50, 68, 0.75NUM.: 45X45, 35, 0.88NUM.: 20X20, 65, 0.90

Figure 6.13. Comparison of actual efficiency predictions for electroformed-wires (ReC = 0.5 to 30). Parameters in legend are mesh size, wire diameter (µm), and fraction of open area (fOA). Note: The gray curves were plotted by correlation

100

Stokes number, Stk0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

Α

0.01

0.1

1

EXPERIMENTALNUMERICALCorrelation (6-4)

Stokes number, Stk

0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

Α

0.01

0.1

1

EXPERIMENTALNUMERICALCorrelation (6-4)

Stokes number, Stk

0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

Α

0.01

0.1

1EXPERIMENTALNUMERICALCorrelation (6-4)

Stokes number, Stk

0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

Α

0.01

0.1

1EXPERIMENTALNUMERICALCorrelation (6-4)

(a) 20×20, 432, 0.436 (b) 64×64, 114, 0.507 (c) 16×16, 457, 0.507 (d) 30×30, 241, 0.511

Stokes number, Stk0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

Α

0.01

0.1

1EXPERIMENTALNUMERICALCorrelation (6-4)

Stokes number, Stk0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

Α

0.01

0.1

1EXPERIMENTALNUMERICALCorrelation (6-4)

Stokes number, Stk

0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

Α

0.01

0.1

1EXPERIMENTALNUMERICALCorrelation (6-4)

(e) 16×16, 406, 0.554 (f) 14×14, 432, 0.581 (g) 16×16, 241, 0.719 Figure 6.14. Comparison of actual efficiency predictions for woven-wires (ReC = 1 to 158). Parameters in legend are mesh size, wire diameter (µm), and fraction of open area (fOA). Note: The gray curves were plotted by correlation Equation (6-4).

101

Stokes number, Stk0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1

EXPERIMENTALNUMERICALCorrelation (6-5)

Figure 6.15. Comparison of actual efficiency predictions for welded-wires (ReC = 10 to 100). Note: The gray curves were plotted by correlation Equation (6-5).

102

103

Figure 6.16. Comparison of actual efficiency predictions for perforated-sheet (ReC = 10 to 575). Parameters in legend are effective slack length (µm) and fraction of open area (fOA).

Stokes number, Stk0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1

EXP.: 425, 0.21EXP.: 1826, 0.51NUM.: 425, 0.21NUM.: 1826, 0.51

Note: The gray curves were plotted by correlation Equation (6-6).

104

Modeling for Standardized Screen Efficiency

Efforts were taken to see if a common basis can be evolved to standardize the

experimental data obtained on the different screen types (as well as the numerical

predictions obtained on the different screen types) that was spread over a wide range of

Stokes numbers depending on their characteristic nature (solidity). As seen in previous

Figures 6.1 to 6.4, the y-intercept and slope increase with the solidity (αA) or,

equivalently, the actual efficiency increase with solidity for a given value of Stokes

number. It was seen that a new parameter “standardized efficiency” (ηSS) that non-

dimensionalizes the actual collection based on the corresponding screen solidity, would

nearly collapse the aerosol deposition data on screens with four different solidity values

to a single performance curve. The standardized screen efficiency, ηSS, is defined as

follows:

A

A

OA

ASS f α

ηηη =−

=1

(6-8)

Aerosol deposition on different screen materials collapsed to a single performance curve

as shown with experimental and numerical data points in Figure 6.17. Especially, in the

case of woven-wire screen the data looks scattered at less than Stokes number 1.0.

With these results, the correlation between the standardized screen efficiency and

Stokes number can be expressed as this form (Sigmoidal, Logistic, 4-parameter)

3)(1)(

2

10.,

xA

ACorrSS

xStkxxStkf

++===

αηη (subscript corr. for correlation) (6-9)

105

Stokes number, Stk0.01 0.1 1 10 100St

anda

rdiz

ed sc

reen

eff

icie

ncy,

ηSS

0.01

0.1

1

65, 0.1035, 0.1268, 0.75160, 0.44

Stokes number, Stk0.01 0.1 1 10 100St

anda

rdiz

ed sc

reen

eff

icie

ncy,

ηSS

0.01

0.1

1

241, 0.28432, 0.42406, 0.45241, 0.49457, 0.49114, 0.49432, 0.56

(a) Electroformed-wire (b) Woven-wire

Stokes number, Stk0.01 0.1 1 10 100St

anda

rdiz

ed sc

reen

eff

icie

ncy,

ηSS

0.01

0.1

1

432, 0.25

Stokes number, Stk0.01 0.1 1 10 100St

anda

rdiz

ed sc

reen

eff

icie

ncy,

ηSS

0.01

0.1

1

1826, 0.49425, 0.79

(c) Welded-wire (d) Perforated-sheet

Figure 6.17. Comparison of standardized screen efficiency predictions for four screens (a. electroformed-wire, b. woven-wire, c. welded-wire, and d. perforated-sheet) to experimental and numerical data. Note: The solid curves were plotted by correlation.

106

To verify the confidence for standardizing all data points using linear regression method

was compared with both measured standardized screen efficiency and correlated

standardized screen efficiency (Figure 6.18) so that R2 value was provided.

Standardized screen efficiency, ηSS

0.01 0.1 1

Stan

dard

ized

scre

en e

ffic

ienc

y, η

SS,C

orr.

0.01

0.1

1

Linear regression (R2=0.977)

Standardized screen efficiency, ηSS

0.01 0.1 1

Stan

dard

ized

scre

en e

ffic

ienc

y, η

SS,C

orr.

0.01

0.1

1

Linear regression (R2=0.948)

(a) Electroformed-wire (b) Woven-wire

Standardized screen efficiency, ηSS

0.01 0.1 1

Stan

dard

ized

scre

en e

ffic

ienc

y, η

SS,C

orr.

0.01

0.1

1

Linear regression (R2=0.992)

Standardized screen efficiency, ηSS

0.01 0.1 1

Stan

dard

ized

scre

en e

ffic

ienc

y, η

SS,C

orr.

0.01

0.1

1

Linear regression (R2=0.979)

(c) Welded-wire (d) Perforated-sheet

Figure 6.18. Plot for verifying the standardizing data points with linear regression method.

107

The constants, x0, x1, x2, and x3 for all screens were provided in Table 6.3 to express a

final correlation between the standardized screen efficiency and Stokes number.

Table 6.3 Values of x0, x1, x2, and x3 in Equation (6-9) obtained by regression analysis. Screen Remark

Type x 0 x 1 x 2 x 3 R 2

Value StdErr Value StdErr Value StdErr Value StdErr

Electroformed -0.714 0.124 1.777 0.136 0.742 0.108 -0.852 0.062 0.992 (0.50≤Stk≤20)

Woven -0.089 0.022 1.156 0.037 0.878 0.023 -0.963 0.040 0.981 (0.08≤Stk ≤12)

Perforated -0.900 0.384 1.858 0.413 0.141 0.058 -0.908 0.132 0.985 (0.15≤Stk ≤7)

x 0 +x 1 /(1+(Stk/x 2 ) x3

As a practical matter, Equation (6-9) can be re-expressed with Stk50 (Table 6.4), the

Stokes number that corresponds to 50% collection efficiency value, as follows:

3)(150

4

1.,

xocorrSS

StkStkx

xx+

+=η (6-10)

Table 6.4 Values of Stk50, and x4 in Equation (6-10). Screen Type Stk 50 x 4

Electroformed 1.829 0.464

Woven 0.913 0.963

Perforated 0.483 0.327

In principle, it is not obvious whether standardized screen efficiency correlates

with only solidity for the screens with different geometrical values even if the same

fraction of open area (fOA) is given. Here, as shown the Figure 6.19 that presented the

108

comparison of actual efficiency with the same solidity, about 49% among the results of

woven-wire screens in this Chapter. From this plot one can easily see that the set of data

are distributed in three different trends (slope and y-intercept), one for 64×64 mesh size

0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1EXP.: 64x64, 114, 0.507

EXP.: 16x16, 457, 0.507

EXP.: 30x30, 241, 0.511

NUM.: 64x64, 114, 0.507

NUM.: 16x16, 457, 0.507

NUM.: 30x30, 241, 0.511

Stokes number, Stk

Figure 6.19. Comparison of actual efficiency predictions for woven-wires to experimental nd numerical data with the same fraction of open area (0.51). Parameters in label are a

mesh size, wire diameter (µm) and fraction of open area.

(wire diameter 114 µm, fraction of open area 0.51), another for 16×16 mesh size (wire

diameter 457 µm, fraction of open area 0.51) and the other for 30×30 mesh size (wire

diameter 241 µm, fraction of open area 0.51). These groups of data appear to follow three

different distributions, particularly for Stokes number less than 1.0. It is known that the

collection process is a combination of several different mechanisms. In the process of

analyzing the original results and its non-dimensional form, it became apparent that

collection characteristics for three screens with the same areal solidity value but different

wire dimensions would be different. This suggests that solidity may not be the only

parameter that influences collection. While Stokes number accounts for the collection due

109

to impaction which is the primary collection mechanism, other mechanisms such as

interception as well as flow effects may contribute to the overall collection. With this

examination, the definition of ηSS can be re-expressed as

HA

SS αA ×=

ηη (6-11)

act as a multiplier to the standardized efficiency presented in Equation (6-11),

as below:

(6-12)

(ηA) is

converted to standardizing basis by defining a standardized screen efficiency, η

The above discussion indicated that a closer introspection of the developed

correlation needed to be undertaken. Subsequently, a correction factor to account for the

two effects was evolved in terms of the respective non-dimensional parameters (R, ReC),

that would

),( CReRfH = : correction factor for standardizing

where R is the interception parameter; ReC is the Reynolds number.

With multiple trial-and-error attempts, we could make standardizing the actual efficiency

data for each screen collapsed. It was seen that when the actual efficiency

SS

)21()1( 31

ββ β

αη

αηη AA RH +×+×=×= (6-13)

where

CAASS Re

β1, β2, and β3 are unknown constant values for a single performance curve.

It was seen that the final form of the standardized screen efficiency, ηSS, as

presented in Equation (6-13) was successfully able to narrow the scatter observed in the

original non-dimensional form presented in Equation (6-10), indicating that these

parameters have a minor effect on collection. Equation (6-13) should be asymptotically

relevant when we obtain the actual efficiency from standardized screen efficiency and

110

orrection factors. The constants, β1, β2, and β3 for all screens were provided in Table

tion.

Table 6.5 Values of β1, β2, and β3 in Equation (6-13) obtained by trial-and-error and the evaluation of linear regression.

c

6.5 to express an interim correla

Screen (1+R β2 )

Type (R=d p /d C )

β2 β3 β4

Electroformed 0.10 -0.03 0.01

(1+β 3/Re Cβ 4 )

(Re C =Ud C /ν )

Woven 0.10 -0.03 0.01

Perforated 0.10 -0.03 0.01

With all previous relationship, the standardized screen efficiency, ηSS,i, can be finally

expressed as

⎥⎤

⎢⎡

+×+×

⎥

⎥

⎦⎢

⎢

⎣

+=×= )21()1()( 31

504

1, β

β βη oiSS R

StkStk

xxHStkf (6-14)

The second product inside braces on the RHS of Equation (6-14) can be conceived as a

correction factor that standardizes the absolute value of the collection efficiency with the

physical and flow parameters associated with the collection process for the different

screens. However, the areal solidity is a dominant factor for standardizing actual

efficiency and the other factors as a minor factors help to collapse all actual efficiencies

to a single performance curve. Aerosol deposi

⎦⎣⎥

⎥⎤

⎢

⎢⎡

+ )(1 3 Cxx

tion on different screen materials collapsed

to a sin

g all data points using linear regression

method, an R2 comparing the measured standardized screen

gle performance curve as shown with experimental and numerical data points, and

final regression curve in Figure 6.20.

To verify the confidence for standardizin

value was obtained by

Re

Stokes number, Stk0.1 1 10 100St

anda

rdiz

ed sc

reen

eff

icie

ncy,

ηSS

0.01

0.1

1

65, 0.1035, 0.1268, 0.75160, 0.44

Stokes number, Stk0.01 0.1 1 10 100St

anda

rdiz

ed sc

reen

eff

icie

ncy,

ηSS

0.01

0.1

1

241, 0.28432, 0.42406, 0.45241, 0.49457, 0.49114, 0.49432, 0.56

Stokes number, Stk0.01 0.1 1 10 100St

anda

rdiz

ed sc

reen

eff

icie

ncy,

ηSS

0.01

0.1

1

1826, 0.49425, 0.79

(a) Electroformed-wire (b) Woven-wire (c) Perforated-sheet

Figure 6.20. Comparison of standardized screen efficiency (Equation 6.13) predictions for screens (a. electroformed-wire, b. woven-wire, and c. perforated-sheet) to experimental and numerical data. Note: The solid curves were plotted by Equation 6.14.

111

112

Standardized screen efficiency, ηSS

0.01 0.1 1Stan

dard

ized

scre

en e

ffic

ienc

y, η

SS,i

0.01

0.1

1

Linear regression (R2=0.989)Reference line (1:1 Ratio)

Standardized screen efficiency, ηSS

0.01 0.1 1Stan

dard

ized

scre

en e

ffic

ienc

y, η

SS,i

0.01

0.1

1

Linear regression (R2=0.963)Reference line (1:1 Ratio)

Standardized screen efficiency, ηSS

0.01 0.1 1Stan

dard

ized

scre

en e

ffic

ienc

y, η

SS,i

0.01

0.1

1

Linear regression (R2=0.982)Reference line (1:1 Ratio)

(1-R2) = 0.011 < 0.113 = wSS (1-R2) = 0.037 < 0.113 = wSS (1-R2) = 0.018 < 0.113 = wSS (a) Electroformed-wire (b) Woven-wire (c) Perforated-sheet Figure 6.21. Plot for verifying the standardizing data points with linear regression method. Comparison between the standardized screen efficiency (ηSS) of Equation 6.13 and correlated standardized screen efficiency (ηSS,i) of Equation 6.14, (a) electroformed-wire, (b) woven-wire, and (c) perforated-sheet.

113

efficiency (ηSS) of Equation (6-13) with correlated standardized screen efficiency (ηSS,i)

of Equation (6-14) and is shown in Figure 6.21. We can see aerosol deposition on

different screen materials collapsed to a single performance curve. There is small

difference between Figure (6-17) and Figure (6-20), which the areal solidity is a

dominant factor for standardizing actual efficiency. However, the other factors help to

collapse all actual efficiencies to a single performance curve, especially the in the lower

Stokes number regions (< 1.0). It is proved by the reference value for which R-square in

Figure (6-21) is better than that in Figure (6-18). However, it was seen that the data could

not be collapsed to a single performance curve even after multiple trial-and-error attempts

and tuning for obtaining the best combination of correction factors. From Figures 6.20 (a

and b) and 6.21(a and b) one can see that the whole set of data seems to be distributed

into two different groups. Therefore, an additional plot is provided by analyzing the

particular trends in Figure 6.22. It was seen that the two groups can be characterized in

terms of a new parameter that can be called as the ‘screen parameter’ which is a product

of the solidity and the circumference of a single wire. Among the parameters listed in

Table 6.6, the wire diameter is probably the most critical of the factors, because the

thickness of the knots where the wires with very small diameter cross over each other

could be considered like the electroformed-wire screen. One (40×40 mesh screen) of

groups on electroformed-wire screen appears to be highest screen parameter (0.009) and

the other group (50×50, 20×20, and 45×45 mesh screens) appears to be almost the same

value (0.001 to 0.002). In the case of woven-wire screen the screen parameter of one

(64×64 and 16×16) of groups is 3 times higher than that of the other. As mentioned

114

Stokes number, Stk0.01 0.1 1 10 100St

anda

rdiz

ed sc

reen

eff

icie

ncy,

ηSS

,i

0.01

0.1

1

Electroformed wireElectroformed wire (Group-A)Electroformed wire (Group-B)Woven wireWoven wire (Group-A)Woven wire (Group-B)

Figure 6.22. Plot for analyzing the characteristic of screen performance as a function of Stokes number. Curves are provided by Equation (6-14).

115

Type fOA αA M Screeninch µm Parameter

(αA×πdw )Electroformed wire 0.006290 160 0.56 0.44 40 0.009

0.002680 68 0.75 0.25 50 0.0020.002565 65 0.90 0.10 20 0.0010.001380 35 0.88 0.12 45 0.001

Woven wire 0.0170 432 0.44 0.56 20 0.0300.0045 114 0.51 0.49 64 0.0070.0180 457 0.51 0.49 16 0.028

0.49 30 0.0150.45 16 0.0220.42 14 0.0220.28 16 0.008

dw

0.0095 241 0.510.0160 406 0.550.0170 432 0.580.0095 241 0.72

Table 6.6. The value of screen parameter for analyzing the characteristic of screen performance in Figure 6.24.

before in Figure 6.19, the collection efficiency at the low screen parameter (about less

than 0.01) would have a low value in the case of the same Stokes number.

Finally, in Figure 6.23 a comparison of aerosol deposition process on the different

screens is presented by Equation (6-14). There is a small difference in the collection

characteristics between wire screens (electroformed-wire, woven-wire and welded-wire

screens) and perforated-sheet screen. It can be explained on the nature of the

manufacturing method.

116

Figure 6.23. Comparison of standardized screen efficiency as a function of Stokes number.

Stokes number, Stk0.01 0.1 1 10 100

Stan

dard

ized

Scr

een

effic

ienc

y, η

SS,i

0.01

0.1

1

ELECTROFORMEDWOVENWELDEDPERFORATED

The solid curves are provided by Equation (6-14).

)1(10

2.3)(56.28.0

RStk

RReLogStk

StkI +⎟⎟

⎠

⎞⎜⎜⎝

⎛ −−−

+=η

[ ]21052.0)8.05.0(16.0 RStkStkRRIR −++=η

22.077.0 23

3

++=

StkStkStk

Iη

StkR

Stk

IR 32

)Re(ln0167.0Reln23.053.11

122+

⎥⎦

⎤⎢⎣

⎡ +−+

=η

The focus of this section is to compare predictions obtained from mathematical

models for the different screens developed in the current study to those of earlier

researchers’ models, obtained mostly for fibrous filters. The comparisons are made to put

the results of the current research in proper perspective as even though there are physical

differences between fibrous filters and screens, the single fiber (wire) approach was used

for describing the physical mechanism of collection. Further, this effort would also serve

to observe the discrepancies in the predictions obtained between the two models (wire

and fiber).

Comparison with Previous Studies

The curve (black color) of ATL (Aerosol Technology Laboratory, TAMU) in

Figure 6.24 represent our final expression (Equation 6-14), and the other curves are

plotted based on our definition in terms of the standardized screen efficiency after

applying for the total efficiency (Equation 2-3 in Chapter II), E, calculated based on the

previous investigators’ solution for the single fiber collection efficiency, η (Tables 2.1 to

2.3 in Chapter II) given below in Equations;

(Landahl & Hermann, Theoretical, 1949) (6-15)

(Davies, Theoretical, 1952) (6-16)

(Schweers et al., Theoretical, 1994) (6-18)

(Suneja & Lee, Numerical, 1974) (6-17)

117

118

Stokes number, Stk0.01 0.1 1 10 100

Stan

dard

ized

Scr

een

effic

ienc

y, η

SS

0.01

0.1

1

10ATL, 2006 (ELECTROFORMED)ATL, 2006 (WOVEN)ATL, 2006 (WELDED)ATL, 2006 (PERFORATED)Landahl & Herrmann, 1949Davies,1952Suneja and Lee, 1974Schweers et al.,1994

Figure 6.24. Comparison of standard screen efficiency for wire screens with those of the previous investigators’ models (ReC = 0.5 to 575).

Here, ∆P = pressure drop across screens; ρa = air density; Uo = face velocity.

Numerical and experimental predictions of pressure drop across the wire screens

(electroformed-wire and woven-wire screens), perforated-sheet screens at different flow

conditions were used to calculate the pressure coefficient (Cp) for flow past the different

screens (Figures 6.25 to 6.27).

Pressure Coefficient Modeling

The previous investigators’ curves were also re-plotted by regression to achieve better

comparison. It can be seen that the previous investigators’ curves over-predict or under-

predict the efficiency depending on the region of Stokes number. Results obtained for all

the screen types (electroformed-wire, woven-wire, welded-wire screens, and perforate-

sheet screen) are provided for comparison. These results suggest that the aerosol

collection characteristic on different models is different and depends on the nature of the

manufacturing process for a typical model (wire or fiber).

At this point the purpose of a new definition for ReC,f is to compare with the

Wakeland and Keolian model (2003). It can be seen that the relationship between the

ReC,f and the pressure coefficient for each screen follows a correlation of the form AReC,f-

1+B, as shown by Wakeland and Keolian (2003), and can be expressed as

221

OaUPCp

ρ∆

=

⎥⎥⎦

⎤

⎢⎢⎣

⎡+×= B

ReAGCp

fCfOA

,

)( OAf ffGOA

(6-19)

, = , µ

ρ coafC

dU=,Re (6-20)

119

Reynolds Number, ReC,f

0.1 1 10 100

Pres

sure

coe

ffic

ient

, Cp

0.1

1

10

100

100040X40, 160, 0.5650X50, 68, 0.7545X45, 35, 0.8820X20, 65, 0.90

Figure 6.25. Pressure coefficient (Cp) as a function of wire Reynolds number (ReC,f) for electroformed-wire screen, between 0.56 and 0.90 fraction of open areas. Note: Symbols are numerical data and solid lines are plotted, based on the correlation Equation (6-20) and Table 6.7.

120

Reynolds Number, ReC,f

1 10 100

Pres

sure

coe

ffic

ient

, Cp

0.1

1

10

100

10000.436, 4320.507, 4570.511, 2410.554, 4060.581, 4320.719, 241

Reynolds Number, ReC,f

1 10 100

Pres

sure

coe

ffic

ient

, Cp

0.1

1

10

100

10000.436, 4320.507, 4570.511, 2410.554, 4060.581, 4320.719, 241

(a) Exp. vs. Num. (b) Exp. vs. Correlation Figure 6.26. Pressure coefficient (Cp) of experimental vs. numerical (a) and experimental vs. correlation (b) as a function of wire Reynolds number (ReC,f) for woven-wire screen, between 0.436 and 0.719 fraction of open area. Note: Symbols are numerical data and solid lines are plotted based on correlation Equation (6-20) and Table 6.7. Parameters in legend are fraction of open area and wire diameter (µm).

121

122

Reynolds Number, ReC,f

1 10 100 1000

Pres

sure

coe

ffic

ient

, Cp

0.1

1

10

100

10000.21, 4250.51, 1826

Reynolds Number, ReC,f

1 10 100 1000

Pres

sure

coe

ffic

ient

, Cp

0.1

1

10

100

10000.21, 4250.51, 1826

(a) Exp. vs. Num. (b) Exp. vs. Correlation Figure 6.27. Pressure coefficient (Cp) of experimental vs. numerical (a) and experimental vs. correlation (b) as a function of effective slack length Reynolds number (ReC,f) for perforated-sheet screen, between 0.21 and 0.51 fraction of open area. Note: Symbols are numerical data and solid lines are plotted based on correlation Equation (6-20) and Table 6.7. Parameters in legend are fraction of open area and wire diameter (µm).

123

OAf

OAf OAfG

OAfG

OAfG

where G is the correction factor. As shown in Equation (6-20), our data was seen to be

best correlated using different G factor, (1±fOA)/fOA. With the correlating function ,

the different data collapse to a single curve that is presented in Figures 6.28 to 6.30 as a

log-log plot of Cp/ versus ReC,f, and compared with those of Wakeland and Keolian

(2003). Table 6.7 summarizes the important deductions obtained from our study and

compares the results to those of Wakeland and Keolian (2003). Figure 6.31 presents the

comparison of Cp/ as a function of Reynolds number for the different screens

(electroformed-wire, woven-wire, and perforated-sheet).

Reynolds Number, ReC,f

0.1 1 10 100

Cp/

G

0.1

1

10

100

1000ATL (G3

fOA)

Wakeland and Keolian (G1fOA

)

Wakeland and Keolian (G2fOA

)

Figure 6.28. Cp/ as a function of wire Reynolds number (Re

OAfG C,f) for electroformed-wire screen, between 0.56 and 0.90 fraction of open area. Note: Solid lines are plotted, based on correlation Equation (6-20) and Table 6.7.

124

Reynolds Number, ReC,f

1 10 100

Cp/

G

0.1

1

10

100

ATL (G3fOA

)Wakeland and Keolian (G1

fOA)

Wakeland and Keolian (G2fOA

)

Figure 6.29. Cp/ as a function of wire Reynolds number (ReOAfG C,f) for woven-wire screen, between 0.436 and 0.719 fraction of open

area. Note: Curves are plotted, based on correlation Equation (6-20) and Table 6.7.

125

Reynolds Number, ReC,f

1 10 100 1000

Cp/

G

0.1

1

10

100ATL (G4

fOA)

Wakeland and Keolian (G1fOA

)

Wakeland and Keolian (G2fOA

)

Figure 6.30. Cp/ as a function of effective slack length Reynolds number (ReOAfG C,f) for perforated-sheet screen, between 0.21 and

0.51 fraction of open area. Note: Curves are plotted, based on correlation Equation (6-20) and Table 6.7.

126

Table 6.7. Summary of the values of (f

OAfG OA) and constants (A and B) for Wakeland and Keolian (2003). and our data (ATL: Aerosol Technology Laboratory at TAMU).

A B Ranges of Re C,f REMARKS

17.0 0.55

11.5 0.40

40.0 1.00 0.2≤Re C,f≤20

(Electroformed-wire)

60.0 2.10 1.0≤Re C,f≤90

(Woven-wire)

70.0 1.00 4.0≤Re C,f≤300

(perforated-sheet)

Wakeland and Keolian (2003)

ATL (2007)

Oscillating Flow0.002≤Re C,f≤400

Steady Flow

2

22 1

OA

OAf

ff

G OA

−≡

OA

OAf

ff

G OA

−≡

13

OAfG

21 1

OA

OAf

ff

G OA

−≡

OA

OAf

ff

G OA

−≡

13

OA

OAf

ff

G OA

+≡

14

127

128

Figure 6.31. Comparison of Cp/ as a function of Reynolds number (ReOAfG C,f) for all screens.

Reynolds Number, ReC,f

0.1 1 10 100 1000

Cp/

G

0.1

1

10

100

1000ElectroformedWovenPerforated

129

CHAPTER VII

APPLICATION TO THE PROBLEM OF

AEROSOL COLLECTION ON A SCREEN

The principal objective of the present research was to develop correlations that

would allow a priori estimation of the aerosol collection efficiency for flow past a screen.

In this section, we provide a two-part demonstration of possible things that can be

accomplished based on the results obtained from the above research.

Part 1: Validation of the developed procedure against experimental data

In the first part, we have considered conditions typical of experimental data obtained on

the 20x20 mesh size screen. Starting from the initial conditions that characterized the

above experiment, we work through the calculations in a step-wise manner to illustrate

the methodology to compute the collection efficiency for one particle size.

STEP 0: Given Initial data: face velocity, mesh size, wire Diameter

Uo = 1.935 m/s, M = 45x45, dw = 35 µm (0.00138-inch), dp = 4.3 µm AD

STEP 1: Estimate the areal solidity (αA) based on the above data as follows.

12.0)4500138.01(1M)1(11 22 =×−−=×−−=−= wOAA dfα (7-1)

STEP 2: Estimate the Stokes number, Stk, defined by Equation (2-4), provided the

interested particle diameter (4.3 µm), air viscosity (0.0000185 kg/(m·s)) and the average

velocity.

130

smUUA

o /20.2)12.01(

935.1)1(

=−

=−

=α

(7-2)

182.3)0254.000138.0(0000185.018

935.1)103.4(1000038.1 26

=×××××××

=−

Stk (7-3)

0.5000015416.0

)0254.000138.0(2.2=

××=wRe (7-4)

12.035

3.4===

w

p

dd

R (7-5)

STEP 3: Estimate the standardize screen efficiency, ηSS,i defined by Equation (6-

14) and Tables 6.3, 6.4, and 6.5 can be calculated,

652.0)0.503.01()12.01(828.1714.0

852.0, +×

⎥⎥

⎤

⎢⎢

⎡

+−=iSSη 3)

182.3(464.01

777.101.0

1.0 =−×⎥

⎦

⎢

⎣×+

(7-6)

STEP 4: Estimate the actual collection efficiency on the screen.

078.012.0684.0, =×=×= AiSSA αηη (7-7)

ded the results in

Table 7-1. Figure 7-1 provides a comparis

We extend the above computation for other particle sizes and provi

on of the reconstructed efficiency curve to

experimental data. It is seen from Figure 7-1 that the agreement to the experiment is

excellent, validating the above procedure.

131

Table 7-1. Result of actual efficiency that was reconstructed based on the application to the case problem-A on a screen (M: 45×45, dw: 35 µm, αA: 0.12) and compared with experimental results.

Correlation Experimentη SS,i η A η A

Stk Rew R η SS,i ×H

0.63 1.0 0.122 0.109 0.013 0.0211.34 0.5 0.254 0.389 0.047 0.0551.88 3.0 0.122 0.500 0.060 0.0642.46 0.5 0.345 0.591 0.071 0.0742.67 1.0 0.254 0.611 0.074 0.0773.14 5.0 0.122 0.648 0.078 0.0853.97 0.5 0.439 0.724 0.087 0.0874.44 0.5 0.465 0.751 0.090 0.0924.91 1.0 0.345 0.766 0.092 0.0906.41 0.5 0.559 0.830 0.100 0.0997.94 1.0 0.439 0.860 0.103 0.1018.02 3.0 0.254 0.850 0.102 0.1038.89 1.0 0.465 0.879 0.106 0.108

12.83 1.0 0.559 0.932 0.112 0.10913.37 5.0 0.254 0.917 0.110 0.11114.76 3.0 0.345 0.934 0.112 0.111

Correction factors(H )

132

Stokes number, Stk0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

ExperimentCorrelation

Figure 7-1. Comparison of the collection efficiency curves as a function of Stokes number reconstructed based on the developed procedure to experimental data. Screen (M: 45×45, dw: 35 µm, αA: 0.12).

Part 2: Use of the developed procedure to generate collection efficiency data for

intermediate screen sizes

We had presented the collection efficiency curves obtained on four different

screens with areal solidity values (0.1, 0.12, 0.25, and 0.44) in Figure 6-13. While the

first two were experimental results, the next two were generated from the validated

numerical procedure. In this section, we consider a couple of screens with solidity values

in the intermediate range, say 0.68 and 0.81 and generate the characteristic collection

efficiency curve for a typical flow condition. For example, consider that the desired flow

133

rate for 0.089 m (3.5-inch) diameter of test section is 1250 L/min (0.02083 m3/s) and

choose a commercially available screen of mesh size (M) 34×34 and wire diameter (dw)

of 131.8 µm (0.00519-inch) (values that are normally provided by the manufacturer).

STEP 0: Given Initial data: Flow rate, mesh size, wire Diameter

Q = 1250 L/min (0.02083 m3/s), M = 34×34, dw = 131.8 µm (0.00519-inch), dp =

10 µm AD

smAQU o /348.3

4)089.0(

02083.02 =

×==π

(7-8)

STEP 1: Estimate the areal solidity (αA) based on the above data as follows.

3217.0)3400519.01(1 2 =×−−=Aα (7-9)

STEP 2: Estimate the Stokes number, Stk, defined by Equation (2-4), provided the

interested particle diameter (10 µm), air viscosity (0.0000185 kg/(m·s))

and the average velocity.

smU

UA

o /95.4)3217.01(

36.3)1(

=−

=−

=α

(7-10)

749.7)0254.000519.0(0000185.018

348.3)1010(1000016.1 26

=×××××××

=−

Stk (7-11)

21.42000015416.0

)0254.000519.0(9.4 36=

××w (7-12) =Re

076.08.131

10==R (7-13)

STEP 3: Estimate the standardize screen efficiency, ηSS, defined by Equation (6-14)

and Tables 6.3, 6.4, and 6.5 can be calculated,

134

833.0)21.4203.01()076.01(

)828.1(464.01714.0

852.0+×

⎥⎥

⎤

⎢⎢

⎡

×++−=SSη

749.7

777.101.0

1.0 =−×

⎥

⎥

⎦⎢

⎢

⎣

(7-14)

STEP 4: Estimate the actual collection efficiency on the screen.

268.03217.0833.0 =×=Aη (7-15)

ollection

efficiency value for different sized partic

Figure

actly similar collection trends, are spaced proportionally apart from their

neighbo

In Table 7-2, we have provided additional calculations that present the c

les, estimated from the above procedure. In

7-2, we have included curves for the intermediate areal solidity values (0.68 and

0.81) generated based on the developed procedure for the two screens (M: 34×34, dw: 132

µm, fOA: 0.68 and M: 36×36, dw: 71 µm, fOA: 0.81), along with the curves presented in

Figure 3.

As observed previously, it can be seen from Figure 7-2 that the new curves

indicate ex

rs, and asymptotically approach a maximum efficiency value that is equal to their

areal solidity. The above result again is physically and intuitively appealing and

demonstrates the soundness of the developed procedure.

135

Table 7-2. Additional calculations that present the collection efficiency value for different sized particles estimated from the application to the problem on a screen (M: 34×34, dw: 132 µm, fOA: 0.68).

d p η SS,i η A

(AD) η SS,i ×Hµm C c Stk Rew R

3 1.054 0.7 42.3 0.023 0.161 0.0525 1.033 2.0 42.3 0.038 0.511 0.1657 1.023 3.8 42.3 0.053 0.694 0.22310 1.016 7.8 42.3 0.076 0.833 0.26816 1.010 19.8 42.3 0.121 0.944 0.304

Correction factors(H )

Stokes number, Stk0.1 1 10 100

Act

ual e

ffic

ienc

y, η

A

0.001

0.01

0.1

1

40x40, 160, 0.5634x34, 132, 06850x50, 68, 0.7536x36, 71, 0.8145x45, 35, 0.8820x20, 65, 0.90

Figure 7-2. Comparison of collection efficiency curves presented in Fig. 6-13 to the new curves reconstructed based on the developed procedure for screens with intermediate solidity values. Screens (M: 34×34, dw: 132 µm, fOA: 0.68 and M: 36×36, dw: 71 µm, fOA: 0.81).

136

CHAPTER VIII

CONCLUSIONS AND FUTURE WORK

The primary objectives of this study were to carry out experimental studies using

commercially available screens (electroformed-wire, woven-wire, welded-wire, and

perforated-sheet) planned to be used as filter media in sampling inlet applications, to

characterize the aerosol deposition process of liquid aerosols. Three-dimensional

numerical simulations were simultaneously performed to assess the capability of

computational fluid dynamics as a predictive tool for the above application. It is seen that

numerical predictions of the aerosol deposition process are in very good agreement with

experimental results over a wide range of wire Reynolds numbers (0.5 < ReC < 575), and

Stokes numbers (0.08 < Stk < 20). This chapter summarizes the important conclusions

that may be drawn based on the results of the present work.

1. The experimental approach used for this screen study was useful for

evaluating collection efficiency. This approach enables the user to get

easily get data for a wide range of conditions.

2. Results of the measurements of both approaches indicate a relationship

between actual efficiency (ηA) and parameters (area solidity and Stokes

number) on the range of Stokes numbers (0.08< Stk <20) and the areal

solidity (0.1< αA <0.79).

3. Many factors influence the screen collection efficiency; however,

geometrical factors (area solidity and characteristic length) and other

137

factors related to flow conditions (Reynolds numbers and Stokes

number), on the screen played an important role.

4. There was a correction factor (H) to standardize all actual efficiencies

for each screen. Non-dimensional parameters (R and ReC) that

standardize the collection efficiency on a particular screen were

identified and used to evolve a new parameter known as standardized

screen efficiency (ηSS) that collapses collection characteristics of

different wire screens to a unique correlation.

5. A mathematical model was developed to express the standardized

screen efficiency (ηSS,i) on different screens as a function of the Stokes

number with correction factors.

6. Our correlation model for wire screens was compared to the

standardized screen efficiency with the earlier researcher’s model.

7. Finally, it was seen the pressure coefficient for flow across the screen

can be expressed as a function of the Reynolds number and the fraction

of open area (fOA). Correlations expressing the actual relationships were

evolved.

8. Additionally, a model was developed to relate pressure coefficient (Cp)

in terms of correction factor ( ) and Reynolds number (ReOAfG C,f).

Recommendations for Future Works

Aerosol penetration through screens has been widely encountered and has a

variety of applications in the filtration and separation of liquid aerosol particles. In order

138

further our understanding of this research area, the following recommendations are made

for future work.

1. Most of the studies that were performed for conditions where the flow is

perpendicular to the screen. It would be useful if new studies in which the

flow is inclined (0< θ <90) to the screen face are performed.

2. Additional work should be performed using solid aerosol particles. In

particular, it would be helpful to understand the experimental methodology,

the extent of loading that could be tolerated by the screen.

3. Further modeling work expanding upon the current correlations, supported by

a more rigorous theoretical basis would be a nice contribution.

139

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143

APPENDIX-1

DEFINITION OF CHARACTERISTIC LENGTH

FOR PERFORATED-SHEET SCREEN

In this section, methodology used to obtain an appropriate characteristic length for

perforated-sheet screens is explained. Table A-1-1 presents the various possible

definitions of characteristic length (CL) that can be conceived for perforated-sheet

screens, computed based on the important geometrical features.

Table A-1-1. Estimation for the proper characteristic length on perforated-sheet screens. Hole diameter Fraction of CS*

Open AreaCL1 CL2** CL3 CL4***

d h f OA d h d h / (√f OA ) C.S.-d h C.S.-0.95d h

inch inch inch inch inch inch

0.0150 0.21 0.031 0.0150 0.033 0.0160 0.017

0.1875 0.51 0.250 0.1875 0.263 0.0625 0.072

*CS: Center-to-Center Spacing**Kanaoka et al., (1978)***Baines and Peterson, (1951)

Group 1 Group 2Characteristic Length

The possible definitions can be organized into two groups, group 1 (CL1 and

CL2) and group 2 (CL3 and CL4), based on either the open area or solid area. CL1 is

defined by the hole diameter of perforated-sheet and CL2 is the length directly calculated

by the fraction of open area. It was seen that collection efficiency curves plotted based on

Stokes number estimates obtained using either definitions of the characteristic length

144

adopted in group 1 were unphysical (Figure A-1-1 a, b). This result indicated that an

alternative definition of the characteristic dimension needs to be evolved. This is the

technical basis for the evolution of the definitions explored in group 2.

Stokes number, Stk0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1

0.21, 0.01500.51, 0.1875

Stokes number, Stk0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A0.01

0.1

1

0.21, 0.0330.51, 0.263

(a) CL1 (b) CL2

Stokes number, Stk0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1

0.21, 0.01600.51, 0.0625

Stokes number, Stk0.01 0.1 1 10

Act

ual e

ffic

ienc

y, η

A

0.01

0.1

1

0.21, 0.0170.51, 0.072

(C) CL3 (d) CL4

Figure A-1-1. Patterns of collection efficiency depended on characteristic length.

145

CL3, defined by CS-dh is exactly the slack length between two holes. However,

the slack length is not consistently uniform for the straight type of perforated sheet screen.

Hence, a new definition of characteristic length, CL4, calculated on the basis of an

imaginary wire screen corresponding to perforated-sheet, as illustrated in Figure A-1-2

was evolved. Based on the above definition, the general form of the equation for the

characteristic length becomes

hdcCSCL ×−= (1)

Where the parameter, c, is a constant value estimated based on the actual geometrical

parameters. Moreover, it can be seen from Figure A-1-1 (c and d) that efficiency curves

plotted based on Stokes number estimates obtained based on group 2 definition of the

Figure A-1-2. Illustration for the calculation of characteristic length on perforated-sheet.

146

characteristic length is physically consistent. In the following demonstration, steps

elaborating the detailed calculation method for the constant, accomplished based on

Equation 3.1 is presented.

For example, consider that the two perforated-sheets, (a) fraction of open area of

0.21, and (b) fraction of open area of 0.51. Mesh size on perforated-sheets which refers

to the number of openings per linear inch was used as the term, 1 over CS (Figure A-1-2).

We work through the calculations to illustrate the methodology to compute the

characteristic length.

STEP 0: Estimate the wire diameter (dw) based on the initial data (fraction of open

area and mesh size) as follows

2)1( Meshdf wOA ×−= defined by Equation (3.1)

(2)

(a) Given Initial data: fraction of open area (0.21), mesh size (1/0.031)

2)031.011(21.0 ×−= wd (3)

CLd w ≡=∴ 016794.0 (4)

(b) Given Initial data: fraction of open area (0.51), mesh size (1/0.250)

2)25.011(51.0 ×−= wd (5)

CLd w ≡=∴ 071464.0 (6)

STEP 1: Estimate a constant value, c, based on the above result as follows

hdcCSCL ×−= defined by Equation (4-6)

147

(a) Given above data in STEP 0 (a) 015.0031.0016794.0 ×−= c (7)

94706.0=∴c (8)

(b) Given above data in STEP 0 (b) 1875.025.0071464.0 ×−= c (9)

95219.0=∴c (10)

The average (11)

STEP 2: Define the final equation of characteristic length on perforated-sheet

screen

(12)

The characteristic length (Equation 12) is applied for perforated-sheet screen in this study.

Additionally, the terms is defined as the effective slack length (les).

of the results, (a) and (b) 95.0=avgc

hdCSCL ×−= 95.0

148

APPENDIX-2

TABLE OF CALCULATION OF COLLECTION EFFICIENCY ON A SCREEN

Table A-2-1 can be used as calculation table for actual efficiency (ηA) depended

on screen types. If a certain Stokes number (Stk) is selected, standardized screen

efficiency (ηSS,i) can be calculated provided correlation equation for each screen type and

then unknown parameters (dp, Uo, dC, and αA) will be obtained for correction factor (R

and ReC). Finally, actually efficiency can estimate.

149

Table A-2-1. Calculation table for standardized screen efficiency (ηSS) and actual efficiency (ηA) depended on screen types.

Screen Actual

Type d p U o d C Stk (1+R) β1 efficiency

(µm) (m/s) (µm) η Α‡

x 0 x 1 x 2 x 3 Stk 50 β1 β2 β3

Electroformed -0.71 1.78 0.46 0.85 1.83 0.10 -0.03 0.01

(0.1<αA <0.44) (0.025<R <0.57)

Woven -0.09 1.16 0.96 0.96 0.91 0.10 -0.03 0.01

(0.28<αA <0.56) (0.007<R <0.18)

Perforated -0.90 1.86 0.33 0.91 0.48 0.10 -0.03 0.01

(0.49<αA <0.79) (0.003<R <0.047)

Note:

†

‡

(1<Re c <268)

(10<Re c <575)

(0.08≤Stk ≤12)

(0.15≤Stk ≤7)

(0.5≤Stk ≤20)

(1+β2 /Re cβ3 )

(0.2<Re c <30)

Unknown parameters

constants for η SS,i†

Standardized

Screen Efficiency

Correction factor (H)

)1( A

oUUα−

=

⎥⎥⎦

⎤

⎢⎢⎣

⎡+×+×

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

++=×= )21()1(

)(1)( 3

1

502

1,

3β

β βηCx

oiSS ReR

StkStk

x

xxHStkf

AiSSA αηη ×= ,

150

APPENDIX-3

SOFTWARE FOR THE DEPOSITION ON SCREENS

The screen deposition program v1.1 developed in Visual Studio has been

modified based on the table of the calculation (Table A-2-1) for standardized screen and

actual efficiencies (ηSS and ηA) depended on screen types. Figure A-3-1 is shown the

captured figure of screen deposition software.

Figure A-3-1. A captured figure of screen deposition software.

151

VITA

Name: TAE WON HAN

Date & Place of Birth: October 5, 1970 Taegu, Korea.

Permanent Address: 1767-1 Shinam 4-Dong, Dong-gu, Taegu, Korea, 701-014

Education: B.S., Mechanical Engineering (February 1997) Keimyung University, Taegu, Korea

M.S., Mechanical Engineering (February 1999) Keimyung University, Taegu, Korea

M.S., Mechanical Engineering (August 2003) Texas A&M University, College Station, Texas

Ph.D., Mechanical Engineering (May 2007) Texas A&M University, College Station, Texas